Question

Choose the Correct answers: 1. A police officer spots a speeding car traveling at 20 m/s (approximately 44 mph) as it passes The officer immediately starts to drive, accelerating from rest at a rate of 5 m/s2. How far will the officer have to drive betore catchıng up to the speeding car? (a) 100 m (b) 80 m (c) 500 m (d) 16 m (e) 160 m 2. A ball is thrown with velocity of 10m/s upwards. If the ball is caught 1 m above its initial position, what is the speed of the ball when it is caught? (a) 5.3 m/s (b) 6.8 m/s (c) 9.0 m/s (d) 10 m/s (e) 22 m/s

Answer 1

1.

Using the formula $x=v_xt+\frac{1}{2}a_xt^2$

For speeding car $v_x=20\,m/s$ and $a_x=0\,m/s^2$

Displacement of speeding car in time $t$$S_1=20*t$

For police car $v_x=0\,m/s$ and $a_x=5\,m/s^2$

Displacement of police car in the same time  $S_2=0*t+\frac{1}{2}*5*t^2$

When they catch up with each other,  $S_1=20*t=S_2=0*t+\frac{1}{2}*5*t^2$

$20*t=\frac{1}{2}*5*t^2$

$t=8\,s$

Displacement of police car $S_2=\frac{1}{2}*5*8^2=160\,m$

Answer is e) 160 m

2.

Using the formula $v_f^2-v_i^2=2a\Delta x$

Initial velocity $v_i=10\,m/s$

Acceleration $a=-9.81\,m/s^2$

Displacement $\Delta x=1\,m$

$v_f^2-10^2=2(-9.81)(1)$

Final velocity $v_f=\sqrt{10^2-2(9.81)}=8.965\approx9.0\,m/s$

Answer is (c) 9.0 m/s