A motorcyclist traveling at 30ms\(^{-1}\) starts to apply his brakes when he is 50m from the traffic light that had just turned red. If he reached the traffic light, his decceleration is
To determine the deceleration of the motorcyclist, we can use the kinematic equation that relates initial velocity, final velocity, acceleration, and distance:
\(v^2 = u^2 + 2as\)
Where: \( v \) = final velocity (0 m/s, since he stops at the traffic light), \( u \) = initial velocity (30 m/s), \( a \) = acceleration (deceleration, which will be negative)
\( s \) = distance (50 m)
Substituting the values into the equation, we rearrange it to solve for \( a \):
\(0 = (30)^2 + 2a(50)\)
Calculating \( (30)^2 \):
\(0 = 900 + 100a\)
Now, rearranging for \( a \):
\(100a = -900\)
\(a = -\frac{900}{100} = -9 \, \text{m/s}^2\)
The deceleration of the motorcyclist is \( \mathbf{9 \, m/s^2} \).
There is an explanation video available below.
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