Car is driving with a speed of 36km/h. Then the car stops completely in 2 seconds. What is the negative acceleration of the car?

I know that this is a very easy problem but I'd be very happy if someone could write the steps of it.

Thank you

1 Answer
Aug 16, 2017

Answer:

#a_x = -6.48xx10^4# #"km/h"^2# #= -5.00# #"m/s"^2#

Explanation:

We're asked to find the acceleration of the car, given its initial speed and how long it takes to stop.

To do this, we can use the equation

#v_x = v_(0x) + a_xt#

where

  • #v_x# is the final velocity of the car

  • #v_(0x)# is the initial velocity of the car

  • #a_x# is the constant acceleration of the car (what we're trying to find)

  • #t# is the time

We know:

  • #v_(0x) = 36color(white)(l)"km/h"#

  • #t = 2# #"s"# #= ul(5.56 xx 10^-4color(white)(l)"h"# (units must be consistent)

  • and the final velocity #v_x = 0#, because it comes to a stop

Plugging i known values:

#0 = 36color(white)(l)"km/h" + a_x(5.56xx10^-4color(white)(l)"h")#

#color(red)(ulbar(|stackrel(" ")(" "a_x = -6.48xx10^4color(white)(l)"km/h"^2 = -5.00color(white)(l)"m/s"^2" ")|)#

The acceleration of the car is thus #color(red)(-6.48xx10^-4color(white)(l)"kilometers per hour per hour"#, which is equal to #color(red)(-5.00color(white)(l)"meters per second per second"#.