Question

A sports car moving at constant speed travels 110m in 5s. If it brakes and comes to a stop in 4.0s, what was its acceleration?

Answer 1

First, we use the distance and time to figure out what the constant velocity of the car initially was before braking.\[v=\frac{ d }{ t }=\frac{ 110 }{ 5 }=22m/s\]Now we apply the kinematic equation that relates initial velocity, final velocity, acceleration, and time. We will take the final velocity to be 0, since the car is coming to a stop. This equation is simply the definition of acceleration: a change in velocity over a given time.\[a=\frac{ v _{f}-v _{i} }{ t }=\frac{ 0-22 }{ 4.0 }=-88m/s^{2}\]The negative sign simply indicates that this is a case of deceleration, where the force acting on the moving car is opposite the direction of initial motion.