Question

A driver of a car traveling at 17.1 m/s applies the brakes, causing a uniform deceleration of 1.5 m/s2.
How long does it take the car to accelerate to a final speed of 13.3 m/s?
Answer in units of s

Answer 1

I know that there are simple physics formulas for this, but I like doing these using simple Calculus.
we are given
a = -1.5 m/s^2 , then
v = -1.5t + c
given: when t=0, v = 17.1
17.1 = 0 + c, c = 17.1, so
v = -1.5t + 17.1

when v = 13.3 ...
13.3 = -1.5t + 17.1
1.5t = 3.8
t = 3.8/1.5 = 2.53 seconds