Question

Barney was driving at 25 mph. A car pulls out 30 ft ahead of him. The coefficient of friction, f, is 0.7. Which statement is true? A Barney hits the car. B Barney stops less than a foot from the car. C Barney misses the car by 3 ft. D Barney's skid marks measure 23 ft.

Answer 1

B Barney stops less than a foot from the car.

Explanation:

From the information given:

The initial speed of barney
`v_o` = 25 mph

Coefficient of friction
`\mu` = 0.7

Recall that

1 mph = 0.447 m/s

Then

`v_o` = 25 × 0.447 m/s

`v_o` = 11.175 m/s

The force of friction acting on the barney is expressed as:

`F = \mu N \\ \\ F = \mu mg`

`ma = \mu mg`

`a = \mu g`

a = 0.7 × 9.8 m/s

a = 6.86 m/s²

Since the force acts in an opposite direction to the motion of Barney, Thus the acceleration must also be negative.

a = -6.86 m/s²

Now;

Suppose Barney stops after traveling a distance (s), so that the final speed is zero.

Then;

Using the kinematic equation;

`v^2 - v_o^2 = 2as`

`0 - (11.17)^2 = 2 * (-6.86) s`

`-124.76 = -13.72 s`

`s = (124.76)/(13.72)`

s = 9.09 m

Recall that;

1 m = 3.28 ft

So;

s = 9.09 m = 9.09 × 3.28 ft

s = 29.81 ft

∴

The distance traveled by the Barney is 29.81 ft which implies that Barney stops less than a foot from the car.