A vehicle starts from rest and accelerates uniformly for 4 seconds to a speed of 8 m/s. Find the distance that the vehicle has traveled during the 4th second. a) 16m b) 9m c) 7m d) 4m

###### Solution. Posted on Saturday, January 17, 2015.

In order to solve this problem, we need to calculate the acceleration. Vf=Vi+a*t , where Vf – the final velocity, Vi – the initial velocity, a – the acceleration and t – the time. 8=0+a*4 So, a=2 m/s^2. The next step will be to calculate the position of the car after the first 3 s and the position of the car after the first 4 s. We will use the following equation: Xf=Xi+Vi*t+a*t^2/2, where Xf – the final position, Xi – the initial position and Vi – the initial velocity. Xf=0+0*3+2*3^2/2=9 m (after the first 3 s) Xf=0+0*4+2*4^2/2=16 m (after the first 4 s) Finally, we could calculate the distance that the vehicle has traveled during the 4th second. We have to subtract the position of the car after the first 3 s from the position of the car after the first 4 s. 16 m – 9 m = 7 m. The answer is c) 7m.