Question

A driver of a car traveling at 14.8 m/s applies the brakes, causing a uniform deceleration of 1.9 m/s2 . How long does it take the car to accelerate to a final speed of 10.0 m/s? Answer in units of s.

Answer 1

`t = 2.53` seconds

Explanation:

Given,

`vecv_i = 14.8(m/s)`, `veca = 1.9 (m/s^2)`, `vecv_f = 10(m/s)`

Looking through the 4 Big Kinematic Equations we've

1. `Deltax=vecv_it+(1/2)at^2`
2. `vecv_f^2=vecv_i^2+2aDeltax`
3. `vecv_f =vecv_i+at`
4. `Deltax = (vecv_i+vecv_f)/2*t`

From these equations and our givens we can use equation number 3. Plugging in the values and solving for `t` yields

`10(m/s) = 14.8(m/s)+(-1.9(m/s^2))*t`
`-4.8(m/s) = -1.9(m/s^2)*t`
`t = 2.53` seconds