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.

1 Answer
Dec 9, 2017

#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