Question

A driver of a car going 90 km/h (change to m/s) suddenly sees the lights of a barrier 40.0 m ahead. It takes the driver 0.75 s before he applies the brakes (this is known as reaction time). Once he does begin to brake, he decelerates at a rate of 10.0 m/s2.
a) Does he hit the barrier?
b) What would be the maximum speed
at which the car could travel and NOT hit the barrier
40.0 m ahead?

Answer 1

Explanation:

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Answer 2

The max u is attained when v becomes zero just before the barrier in the $20.61\frac{m}{s}$ .

Explanation:

$u=90\frac{km}{h}$

$=\frac{90*1000}{3600} \frac{m}{s}$

$=25\frac{m}{s}$

Distance travelled till the driver hits the brake

$s_{1}=25\frac{m}{s} *0.75s$

$=18.75m$

Distance left between car and barrier

$=40-18.75m$

$=21.25m$

Now, a$=-10\frac{m}{s}$

$V^{2}=u^{2}+2as$

$=625-425$

$V^{2}=200$

$V=\sqrt{200} \frac{m}{s}$

hence, the car will hit the barrier

Max u is attained when v becomes zero just before the barrier

$V^{2}=U^{2}-425$

$0=U^{2}-425$

$U^{2}=425$

$U=\sqrt{425} \frac{m}{s}$

$U=20.61\frac{m}{s}$