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A stuntman drives a car of mass 1125 kg east with a speed of 20 m/s. If the car accelerates at a rate of -2 m/s², how long will it take the car to go 50 m?

A) 25 s
B) 20 s
C) 30 s
D) Information not available

1 Answer

3 votes

Final answer:

Using the equations of motion and quadratic formula to solve for time, the car will travel 50 m in approximately 12.245 seconds. None of the options provided in the question match this answer, therefore the correct choice is 'Information not available'.

Step-by-step explanation:

To find out how long it will take the stuntman's car to go 50 m, we need to use the equations of motion for a body with constant acceleration. The car is decelerating, which is indicated by the negative acceleration (-2 m/s²). We can use the following equation of motion:

s = ut + ½ at²

where:

  • s = distance
  • u = initial speed
  • a = acceleration
  • t = time

Plugging in the known values:


50 m = (20 m/s)t + ½ (-2 m/s²)t²

This can be rearranged into a quadratic equation:


1 m/s²t² - 20 m/st + 50 m = 0

To find t, we can use the quadratic formula:

t = ± (square root of ((-b)² - 4ac)) / (2a)

Substituting our values in:

t = ± (square root of ((20)² - 4(1)(-50))) / (2(1))

t = ± (square root of (400 + 200)) / 2

t = ± (square root of 600) / 2

The square root of 600 is approximately 24.49, so:

t = ± 24.49 / 2

t = ± 12.245

Since time cannot be negative, the positive value is the correct answer:

t = 12.245 s

So, the correct answer for the time it will take the car to go 50 m is not provided in options A) 25 s, B) 20 s, C) 30 s, hence D) Information not available is the correct answer.

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