Question

A particle moves along straight line on y axis .The distance of the particle from O varies with time and is given by: y=20t-t^2.the distance travelled by the particle before it momentarily comes to rest is
1. 200m
2. 100m
3. 50m
4. 150m

Answer 1

v = dy/dt = 20 - 2t
when it comes to rest there it's velocity is 0
0=20-2t
Hence, 2t = 20
So, t=2s
Using the value of time in given equation
So 20t-t^2 =20(10)- (10)^2
=200-100
=100m
Hence the distance travelled is 100m

Answer 2

Answer : d = 100 m

Explanation :

The distance of the particle from O varies with time and it is given by :

$y=20t-t^2$........(1)

When object comes to rest, the velocity becomes zero.

Also, $v=\dfrac{dy}{dt}$

So, $v=20-2t$

$0=20-2t$

$t=10\ s$

Put the value of time in equation (1) and the distance travelled by the particle becomes :

$y=20(10)-(10)^2$

$y=100\ m$

Hence, the correct option is (2) i.e. distance travelled by the particle before it momentarily comes to rest is 100 m.