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12 January, 16:26

The driver of a car slams on the brakes, causing the car to slow down at a rate of

26ft/s2 as the car skids 256ft to a stop.

How long does the car take to stop?

What was the car's initial speed?

ft/s 4

+1
Answers (1)
  1. 12 January, 19:28
    0
    A. The time taken for the car to stop is 3.14 secs

    B. The initial velocity is 81.64 ft/s

    Explanation:

    Data obtained from the question include:

    Acceleration (a) = 26ft/s2

    Distance (s) = 256ft

    Final velocity (V) = 0

    Time (t) = ?

    Initial velocity (U) = ?

    A. Determination of the time taken for the car to stop.

    Let us obtain an express for time (t)

    Acceleration (a) = Velocity (V) / time (t)

    a = V/t

    Velocity (V) = distance (s) / time (t)

    V = s/t

    a = s/t^2

    Cross multiply

    a x t^2 = s

    Divide both side by a

    t^2 = s/a

    Take the square root of both side

    t = √ (s/a)

    Now we can obtain the time as follow

    Acceleration (a) = 26ft/s2

    Distance (s) = 256ft

    Time (t) = ... ?

    t = √ (s/a)

    t = √ (256/26)

    t = 3.14 secs

    Therefore, the time taken for the car to stop is 3.14 secs

    B. Determination of the initial speed of the car.

    V = U + at

    Final velocity (V) = 0

    Deceleration (a) = - 26ft/s2

    Time (t) = 3.14 sec

    Initial velocity (U) =.?

    0 = U - 26x3.14

    0 = U - 81.64

    Collect like terms

    U = 81.64 ft/s

    Therefore, the initial velocity is 81.64 ft/s
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