Question

A car travels with a uniform velocity of 30 m/s for 10 seconds and then comes to rest with a uniform retardation in the next 5 seconds. Calculate the total distance travelled by the car and its retardation.

Answer 1

Uniform motion
Velocity: \((30 \text{ m/s})\)
Time: \((10 \text{ s})\)
Distance: \(d_1 = v \times t = 30 \times 10 = 300 \text{ meters}\)

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Uniform retardation:
Initial velocity: \((30 \text{ m/s})\)
Final velocity: \((0 \text{ m/s})\)
Time: \((5 \text{ s})\)
Retardation: \(a = \frac{v - u}{t} = \frac{0 - 30}{5} = -6 \text{ m/s}^2\)
Distance: \(s = ut + \frac{1}{2} a t^2 = 30 \times 5 + \frac{1}{2} \times (-6) \times (5)^2 = 150 - 75 = 75 \text{ meters}\)

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Total distance
\(d_{\text{total}} = d_1 + s = 300 + 75 = 375 \text{ meters}\)

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So, the total distance traveled by the car is 375 meters and the retardation is 6 m/s².