Question

A bird flies for 4 s with a velocity of $|t-2|$ m/s in a straight line, where t is time in seconds. It covers a distance of

• A. 2m
• B. 4m
• C. 6m
• D. 8m

Answer 1

The correct option is B

4m

The velocity time graph for given problem is shown in the figure.

Now draw speed time graph to find distance.

It will be exactly the same.

Distance travelled S = Area under curve = 2 + 2 = 4m

Velocity is uniformly decreasing from t = 0 to t = 2

So we can say that the acceleration is constant which is $\frac{△v}{△t}=\frac{0-2}{2}=-1m/s^2$

u = 2 m/s v = 0 m/s

distance covered $v^2-u^2=2as$

$s=\frac{4}{2}=2m$

Similarly in t = 2 to t = 4 duration

acceleration = $\frac{△v}{△t}=\frac{2}{2}=1m/s^2$

distance covered

$v^2-u^2=2as$

4 = 2s

s = 2m

so total distance = 4m

here solving by graph is much easier

i.e., area under the v - t curve gives displacement