Question

a ball moves on a smooth floor in a straight line with a uniform velocity 10 m/s for 6 s. At t=6s the ball hits a wall and comes back along the same line to the starting point with same speed. draw the velocity-time graph and use it to find the total distance travelled by the ball and its displacement.

Answer 1

a ball moves on a smooth floor in a straight line with a uniform velocity 10m/s for 6sec.

at t = 6sec the ball hits a wall and comes back along the same line to the starting point with the same speed.

if we assume, initial velocity of ball is $\vec{u}=10\hat{i}$[ along positive x-axis ]

then, after hitting velocity of ball will be $\vec{v}=-10\hat{i}$

so, the velocity-time graph of first case is straight line parallel to x - axis and lies positive direction of y-axis and second case is also a straight line parallel to x-axis but lies negative direction of y-axis as shown in figure.

total distance travelled by ball = |ut| + |vt|

= |10m/s × 6s | + |-10m/s × 6s|

= 60m + 60m = 120m

displacement = ut + vt

= 10i m/s × 60s + (-10i) m/s × 60s

= 60i m - 60i m

= 0

Answer 2

Answer:

Distence travelled in first 6s = velocity×time

=10m/s×6

=60m/s

Distance travell in next 6s = velocity×time

=10m/s×6

=60m/s

Total distance travelled in 12s = (60+60)m = 120m

Total displacement = 0, at the ball returns its starting point.