A particle is moving in a straight line with a constant acceleration. It changes its velocity from 10 m/s to 20 m/s, while passing through a distance of 135 m in t seconds. The value of t is:
(a) 10
(b) 1.8
(c) 12
(d) 9
Answer (1)
To solve this problem, we can use the equations of motion for a particle moving with constant acceleration. The relevant equation here relates the initial velocity v i , final velocity v f , acceleration a , distance s , and time t .
The formula for the relation between these is:
s = 2 ( v i + v f ) ⋅ t
where:
s is the distance traveled (135 m)
v i is the initial velocity (10 m/s)
v f is the final velocity (20 m/s)
t is the time in seconds
This formula is derived from the average velocity, where the average velocity in uniformly accelerated motion is the average of the initial and final velocities.
Substitute the given values into the equation:
135 = 2 ( 10 + 20 ) ⋅ t
Simplifying the equation:
135 = 2 30 ⋅ t
135 = 15 t
To find t , divide both sides by 15:
t = 15 135
t = 9
So, the time t taken by the particle is 9 seconds.
Therefore, the correct answer is option (d) 9.
