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# If a ball is thrown vertically upwards and the height ‘s’ reached in time ‘t’ is given by $s = 22t - 11{t^2}$, then the total distance travelled by the ball is $(A)$ 44 units $\left( B \right)$ 33 units $\left( C \right)$ 11 units$\left( D \right)$ 22 units  Verified
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Hint: Use Velocity =$\dfrac{{ds}}{{dt}}$, from this obtain the value of t and substitute this value into the given distance equation to find the total distance.

It is given to us that Height ‘s’ is reached by the ball in time t is given by
$s = 22t - 11{t^2}$
Now on differentiating with respect to t on both sides,
We get velocity, v=$\dfrac{{ds}}{{dt}} = 22 - 22t$
At the topmost point, velocity becomes zero and so
$\Rightarrow 22 - 22t = 0$
And hence on simplification, we have
$\Rightarrow 22=22t$
$\Rightarrow t=1$
Thus time taken for an upward journey is 1 unit.
So distance travelled in upward journey is obtained by putting the value of t in the given distance equation, we have
$s=22-11.1=11$ units
The same distance would be travelled by the ball in its return journey and thus,
The total distance travelled by the ball becomes 22 units.
Here option (D) is the correct answer.

Note: In these type of questions first we have to find the velocity and for that we’ll differentiate the given equation and hence on solving the differentiated equation we’ll have the value of t and hence on putting that value over given equation we’ll have the distance travelled in upward journey and since the same distance will be travelled by the ball in its return journey so on adding booth the distances we’ll have our answer.