RECTILINEAR KINEMATICS: Constant AccelerationGeneral equations for rectilinear motion:When the acceleration is constant, each of the three kinematic equation above may be integrated toobtain the formulas that relate acceleration, a, velocity, v, displacement, s and time, t.
Example:A car has an initial velocity of 20 m/s and an acceleration of -1.0 m/s2. Find the following: a. The velocity after 10s and after 50s. b. The displacement after the first 10s and after the first 50s from the moment the acceleration beings. c. The distance of the car when it comes to stop.
Problems: 1. A Porche reaches a velocity of 42.0 kph from a standing start in 15.5 s. What distance does it cover while doing so? [Ans. 90.4 m] 2. The driver of a train travelling at 30m/s applies the brakes when he passes an amber signal. The next signal is 1.5 km down the track and the train reaches it 75s later. Assuming a uniform acceleration, find the velocity of the train at the second signal. [Ans. 10 m/s] 3. A car is stationary in front of a red traffic light. As the light turns green, a truck goes past at a constant velocity of 15 m/s. At the same moment, the car begins to accelerate at 1.25 m/s 2. When it reaches 25 m/s, the car continues at this velocity. When does the car pass the truck? How far have they gone from the traffic light at that time? [Ans. 25s, 380 m] 4. The brakes of a car moving at 14m/s are suddenly applied and the car comes to stop in 4.0 s. (a) What was its acceleration? (b) How long would the car take to come to a stop starting from 20m/s with the same acceleration? (c) How long would the car take to slow down from 20m/s to 10m/s with the same acceleration? 5. A car starts from rest with an acceleration of 0.40m/s2. One minute later the acceleration stops, and the car continues at constant velocity for 5.0min. The car’s brakes are then applied, and the car comes to rest in 2.0min with a uniform deceleration. (a) Show the car’s motion on a velocity- time graph. (b) Find the total displacement of the car.