IIT JEE Kinematics Questions

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Problem 1.

A train covers 60 miles between 2 p.m. and 4 p.m. How fast was it going at 3 p.m.?


Problem 2.

Is it possible that the car could have accelerated to 55mph within 268 meters if the car can only accelerate from 0 to 60 mph in 15 seconds?

Problem 3.

A car travels up a hill at a constant speed of 37 km/h and returns down the hill at a constant speed of 66 km/h. Calculate the average speed for the whole trip.

Problem 4.

An archer shoots an arrow with a velocity of 30 m/s at an angle of 20 degrees with respect to the horizontal. An assistant standing on the level ground 30 m downrange from the launch point throws an apple straight up with the minimum initial speed necessary to meet the path of the arrow. What is the initial speed of the apple and at what time after the arrow is launched should the apple be thrown so that the arrow hits the apple?

Problem 5.

A box sits on a horizontal wooden board. The coefficient of static friction between the box and the board is 0.5. You grab one end of the board and lift it up, keeping the other end of the board on the ground. What is the angle between the board and the horizontal direction when the box begins to slide down the board?


Problem 6.

A 8 kg block is at rest on a horizontal floor. If you push horizontally on the 8 kg block with a force of 20 N, it just starts to move.

(a) What is the coefficient of static friction?

(b) A 10.0 kg block is stacked on top of the 8 kg block. What is the magnitude F of the force, acting horizontally on the 8 kg block as before, that is required to make the two blocks start to move?

Problem 7.

A car is accelerating at . Find its acceleration in .

Problem 8.

We drive a distance of 1 km at 16 km/h. Then we drive an additional distance of 1 km at 32 km/h. What is our average speed?

Problem 9.

An airliner reaches its takeoff speed of 163 mph in 36.2 s. What is the magnitude of its average acceleration.

Problem 10.

A car is initially traveling due north at 23 m/s.
(a) Find the velocity of the car after 4 s if its acceleration is due north.
(b) Find the velocity of the car after 4 s if its acceleration is instead due south.

Problem 11.

From the dimensional analysis find the time t it takes for a ball to fall from a height h.

Problem 12.

You are driving along the street at the speed limit (35mph) and 50 meters before reaching a traffic light you notice it becoming yellow. You accelerate to make the traffic light within the 3 seconds it takes for it to turn red. What is your speed as you cross the intersection? Assume that the acceleration is constant and that there is no air resistance.

Problem 13.

How high can a human throw a ball if he can throw it with initial velocity 90 mph.

Problem 14.

Mr. Letourneau is flying his broom stick parallel to the ground. He undergoes two consecutive displacements. The first is 100 km 10 degrees west of north, and the second is 120 km 50 degrees east of north. What is the magnitude of the broom stick's displacement?

Problem 15.

In reaching her destination, a backpacker walks with an average velocity of 1 m/s, due west. This average velocity results, because she hikes for 6 km with an average velocity of 3 m/s due west, turns around, and hikes with an average velocity of 0.3 m/s due east.

How far east did she walk (in kilometers)?

Problem 16.

It takes you 9.5 minutes to walk with an average velocity of 1.2 m/s to the north from the bus stop to museum entrance. What is your displacement?

Problem 17.

What is 3.3 slug in kilograms?

Problem 18.

An athlete swims the length of a 50.0-m pool in 20.0s and makes the return trip to the starting position in 22.0s. Determine her average velocities in

(a) the first half of the swim,

(b) the second half of the swim, and

(c) the round trip.

Problem 19.

A speedboat increases its speed uniformly from 20 m/s to 30 m/s in a distance of 200m. Find

(a) the magnitude of its acceleration and

(b) the time it takes the boat to travel the 200-m distance.

Problem 20.

The car drives straight off the edge of a cliff that is 57 m high. The investigator at the scene of the accident notes that the point of impact is 130 m from the base of the cliff. How fast was the car traveling when it went over the cliff?

Problem 21.

An aircraft has a lift-off of 120km/h.

(a) What minimum constant acceleration does the aircraft require if it is to be airborne after a takeoff run of 240m?

(b) How long does it take the aircraft to become airborne?

Problem 22.

A ball is thrown vertically upward with a speed of 25.0m/s.

(a) How high does it rise?

(b) How long does it take to reach its highest point?

(c) How long does the ball take to hit the ground after it reaches its highest point?

(d) What is its velocity when it returns to the level from which it started?

Problem 23.

A tortoise and a hare are in a road race to defend the honor of their breed. The tortoise crawls the entire 1000 meters at a speed of 0.2 m/s. The rabbit runs the first 200 meters at 2 m/s, stops to take a nap for 1.3 hours, and awakens to finish the last 800 meters with an average speed of 3 m/s. Who wins the race and by how much time?

Problem 24.

The slowest animal ever discovered is a crab found in the Red Sea that travels an average speed of 5.7 km/year. How long will it take this crab to travel 1 meter?

Problem 25.

A "moving sidewalk" in a busy airport terminal moves 1 m/s and is 200 m long. A passenger steps onto one end and walks, in the same direction as the sidewalk is moving, at a rate of 2.0 m/s relative to the moving sidewalk. How much time does it take the passenger to reach the opposite end of the walkway?

Problem 26.

Assume it takes 8 minutes to fill a 35.0 gal gasoline tank. (1 U.S. gal = 231 cubic inches)
(a) Calculate the rate at which the tank is filled in gallons per second.
(b) Calculate the rate at which the tank is filled in cubic meters per second.
(c) Determine the time interval, in hours, required to fill a volume at the same rate.

Problem 27.

A plane flies 955 km due east, then turns due north and flies another 469 km. Draw an x-y axis at the starting point with the positive x-axis pointing east, and determine the polar coordinates of the plane's finale position.

Problem 28.

A car travels east at 89 km/h for 1 h. It then travels 26° east of north at 141 km/h for 1 h.

(a) What is the average speed for the trip?

(b) What is the average velocity for the trip?

Problem 29.

(a) If a particle's position is given by (where t is in seconds, and x is in meters), what is it's velocity at t=1s?

(b) what is it's speed at t=1s?

(c) Is there ever an instant when the velocity is 0? If so, give the time.

Problem 30.

The captain of a plane wishes to proceed due west. The cruising speed of the plane is 245 m/s relative to the air. A weather report indicates that a 38-m/s wind is blowing from the south to the north. In what direction, measured to due west, should the pilot head the plane relative to the air?

Problem 31.

A missile is launched into the air at an initial velocity of 80 m/s. It is moving with constant velocity until it reaches 1000m, when the engine fails.

(a) How long does it take it to reach 1000m?

(b) How high does the missile go?

(c) How long does it take for it to fall back to the earth?

(d) How long does it stay in the air?

(e) How fast is it going when it hits the ground?

Problem 32.

The highest barrier that a projectile can clear is 14 m, when the projectile is launched at an angle of 30.0 degrees above the horizontal. What is the projectile's launch speed?

Problem 33.

A rocket is fired vertically upwards with initial velocity 80 m/s at the ground level. Its engines then fire and it is accelerated at until it reaches an altitude of 1000 m. At that point the engines fail and the rocket goes into free-fall. Disregard air resistance.

(a) How long was the rocket above the ground?

(b) What is the maximum altitude?

(c) What is the velocity just before it collides with the ground?

Problem 34.

An object is fired straight up at a speed of 9.8m/s. Compute its maximum altitude and the time it takes to reach that height. Ignore air resistance.

Problem 35.

A rock is dropped from rest into a well.

(a) The sound of the splash is heard 4 s after the rock is released from rest.

How far below to top of the well is the surface of the water? (the speed of sound in air at ambient temperature is 336m/s).

(b) If the travel time for the sound is neglected, what % error is introduced when the depth of the well is calculated?

Problem 36.

A ball is thrown upward with initial velocity v. What is the change in speed on the way up? What is the change in speed on the way down? Disregard air resistance.

Problem 37.

A displacement, s, of an object as a function of time, t, is given by

a) Find an expression for the acceleration of the object

b) Explain why this expression indicates that the acceleration is not constant

Problem 38.

Snow is falling vertically at a constant speed of 3 m/s. At what angle from the vertical do the snowflakes appear to be falling as viewed by the driver of a car traveling on a straight, level road with a speed of 60 km/h?

Problem 39.

A dart is thrown horizontally with an initial speed of 10 m/s toward point P, the bull's-eye on a dart board. It hits at point Q on the rim, vertically below P, 0.2 s later. What is the distance PQ? How far away from the dart board is the dart released?

Problem 40.

A boy walks to the store using the following path: 0.4 miles west, 0.2 miles north, 0.3 miles east. What is his total displacement? That is, what is the length and direction of the vector that points from her house directly to the store?

Problem 41.

A motor scooter travels east at a speed of 13 m/s. The driver then reverses direction and heads west at 17 m/s. What was the change in velocity of the scooter?

Problem 42.

A bicycle travels 3.2 km due east in 0.1 h, the 3.2 km at 15.0 degrees east of north in 0.21 h, and finally another 3.2km due east in 0.1 h to reach its destination. The time lost in turning is negligible. What is the average velocity for the entire trip?
Problem 43.

A swimmer dived off a cliff with a running horizontal leap. What must his minimum speed be just as he leaves the top of the cliff so that he will miss the ledge at the bottom which is 2 m wide and 9 m below the top of the cliff?

Problem 44.

A ferries wheel with radius 20 m which rotates counterclockwise, is just starting up. At a given moment, a passenger on the rim of the wheel and passing through the lowest point of his circular motion is moving at 3.00m/s and in gaining speed at a rate of .

Find the magnitude of the passenger's acceleration at the instant.

Problem 45.

In an action film hero is supposed to throw a grenade from his car, which is going 90.km/h, to his enemy's car, which is going 110 km/h. The enemy's car is 15.8 m in front of the hero's when he lets go of the grenade. If the hero throws the grenade so its initial velocity relative to him is at an angle of 45(degree) above the horizontal, what should the magnitude of the initial velocity be? The cars are both traveling in the same direction on a level road. Ignore air resistance.

Find the magnitude of the velocity both relative to the hero and relative to the earth.

Problem 46.

A flowerpot falls from a windowsill 25.0 m above the sidewalk.

(a) how fast is the flowerpot moving when it strikes the ground?

(b) how much time does a passerby on the sidewalk below have to move out of the
way before the flowerpot hits the ground?


Problem 47.

A tennis ball is thrown vertically upward with an initial velocity of +8.0 m/s.

(a) what will the ball\'s speed be when it returns to its starting point?

(b) how long will the ball take to reach its starting point?

Problem 48.

Problem 4.14 of Serway & Jewett: A firefighter, a distance d from a burning building,
directs a stream of water from a fire hose at angle above the horizontal. If the initial
speed of the stream is , at what height h does the water strike the building?

Problem 49.

If it takes a player 3 seconds to run from the batter's box to the first base at an average speed of 6.5 m/s, what is the distance she covers in that time?

Problem 50.

A car goes down a certain road at an average speed of 40 km/h and returns along the same road at an average speed of 60 km/h. Calculate the average speed for the round trip.

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Answered By StudyChaCha Member