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A car is moving at a speed of 40m/s. The driver suddenly sees a goat crossing the road 100 meters ahead. He applies the brakes and brings the car to rest in 4 seconds, assuming uniform deceleration. Determine whether the car will cross the road in time.

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2 parts
a

10 m/s210 \, \text{m/s}^2

b

not hit the goat\text{not hit the goat}

Step-by-step solution

6 steps

It looks like you're asking for the solution to the problem described in the text, which is different from the partial work shown above it. Let's solve that one.

Given:
Initial velocity of the car, u=40 m/su = 40 \, \text{m/s}
Distance to the goat, d=100 md = 100 \, \text{m}
Time taken to stop, t=4 st = 4 \, \text{s}
Final velocity (car comes to rest), v=0 m/sv = 0 \, \text{m/s}

Part a· 3 steps

Determine the deceleration of the car.

  1. Use the kinematic equation relating initial velocity, final velocity, acceleration, and time.

    v=u+atv = u + at

  2. Substitute the given values into the equation.

    0 m/s=40 m/s+a(4 s)0 \, \text{m/s} = 40 \, \text{m/s} + a(4 \, \text{s})

  3. Solve for aa.

    −40 m/s=4a s-40 \, \text{m/s} = 4a \, \text{s} a=−40 m/s4 sa = \frac{-40 \, \text{m/s}}{4 \, \text{s}} a=−10 m/s2a = -10 \, \text{m/s}^2

    The deceleration is 10 m/s210 \, \text{m/s}^2. The negative sign indicates deceleration.
    The deceleration is 10 m/s2\boxed{10 \, \text{m/s}^2}.

Part b

not hit the goat\text{not hit the goat}

Determine whether the car will hit the goat.

  1. Calculate the stopping distance (ss) using the kinematic equation relating initial velocity, final velocity, and time.

    s=(u+v)2ts = \frac{(u+v)}{2}t

  2. Substitute the given values into the equation.

    s=(40 m/s+0 m/s)2(4 s)s = \frac{(40 \, \text{m/s} + 0 \, \text{m/s})}{2}(4 \, \text{s}) s=40 m/s2(4 s)s = \frac{40 \, \text{m/s}}{2}(4 \, \text{s}) s=(20 m/s)(4 s)s = (20 \, \text{m/s})(4 \, \text{s}) s=80 ms = 80 \, \text{m}

  3. Compare the stopping distance with the distance to the goat.

    Stopping distance s=80 ms = 80 \, \text{m}
    Distance to goat d=100 md = 100 \, \text{m}
    Since 80 m<100 m80 \, \text{m} < 100 \, \text{m}, the car stops before reaching the goat.
    The car will not hit the goat\boxed{\text{not hit the goat}}.

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