Here are a selection of kinematic questions for you to try! Using what you have learned in previous lectures 2a and 2b - try these examples.

The techniques of finding slopes (how quickly something changes in time or space) and finding areas (the effect of something through time or space) should be applied to accelerations that are linear in time.

More tutorial questions

E1. A springbok sees a cheetah and runs away at a constant speed of 13 m s^-1. When the springbok is 19 m away the cheetah accelerates (constantly) from rest towards it and reaches a speed of 19.4 m s^-1 in 2 s. The cheetah then travels at a constant speed towards the springbok for 4 s. Find
(a) the acceleration of the cheetah during the first 2 s.
(b) the distance travelled by the cheetah in the 6 s.
(c) the distance between the springbok and the cheetah at the end of the 6 s.

E2. By extending its legs a flea can accelerate upwards withan average acceleration of 1200 m s^-2! Assume humans could have this constant acceleration over 0.54 m to create a vertical take off speed. Find
(a) the speed at which they would take off from the ground.
(b) the vertical height that they would reach.

E3. The gravitational acceleration on the surface of Mars is estimated at 3.8 m.s^-2. A lead ball falls from rest and acquires a speed of 34.2 km.hr^-1 just before it hits the surface of Mars. Find
(a) the time taken in the fall.
(b) the height from which the lead ball fell to give it this speed.

E4. A Cessna 150 aircraft needs to reach a speed of 126 km.hr^-1 in order to lift off the ground. The effective runway length is 245m. Assume a constant acceleration. Find
(a) the time taken to reach the lift-off speed.
(b) the minimum (constant) acceleration required to achieve lift-off on the runway.

E5. A car accelerates uniformly from rest along a straight road. It reaches a maximum speed of 108 km hr^-1 in one minute, after which it travels with constant speed for 3 minutes. Then it comes to rest (with uniform deceleration) in 15 seconds.
(a) Sketch a speed-time graph for the motion, labelling axes with quantities, SI units and relevant values.
(b) Calculate the total distance travelled by the car.
(c) Calculate the average speed of the car for the whole motion.

E6. A Porsche racing car accelerates from rest, uniformly at 12 ms^-2 for 2 s, then maintains constant speed for 1 s, and then decelerates uniformly, coming to rest in a further 3 s.
(a) Sketch an acceleration-time graph for the motion, labelling axes with quantities, SI units and relevant values.
(b) Calculate the speed of the car at 4 seconds from the start.
(c) Calculate the total distance travelled by the car in the 6 seconds.

E7. A train driver in a passenger train moving at 32 m s^-1 rounds a corner and sees a freight train 50m ahead on the same straight track and moving in the same direction with a speed of 20 m s^-1. The brakes are applied on the passenger train giving the passenger train a constant deceleration of 1.46 m s^-2. The freight train continues at constant speed.
(a) Sketch graphs showing for both trains:- speed vs time and position vs time, and
(b) determine if there will be a collision.

E8. At the instant a traffic light turns green a car accelerates from rest at a constant rate of 2.2 m.s^-2. At the same instant, a truck overtakes the car, traveling with a constant speed of 16.5 m.s^-1. Find
(a) how far from the traffic light the car overtakes the truck, and
(b) how fast the car is traveling when it overtakes the truck.

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