Question

A particle moving with uniform acceleration along
x-axis crosses the points x = 2 m and x = 7 m with
velocities 5 ms-1 and 15 ms-' respectively. The
velocity with which it crosses point x = 3 m is​

Answer 1

Answer:

8.06 m/s (approx)

Explanation:

Assuming that the particle starts motion at x= 2 m,

Initial position= 2 m

Final position= 7 m

distance covered (s)= 7-2= 5 m

u= 5 m/s

v= 15 m/s

Using v²= u²+2 as

15²= 5²+2*a*5

225=25+10a

10a= 225-25

10a=200

a=20 m/s²    ----------(i)

Now,

at point x= 3 m

distance covered (s)= 3-2= 1 m   [since 2 m is the starting point]

u=5 m/s

a= 20 m/s²   [from (i) ]

We have to find velocity with which the particle crosses x=3 m

Thus,

v²= u²+2 as

v²= 5²+2*20*1

v²= 25+40

v²= 65

v= √65

v= 8.06 m/s

(Here, I have assumed that the particle starts its motion at x= 2 m. But maybe the particle is starting at origin, that is, x= 0 m. But if I assume that the particle starts at origin, the acceleration will become non-uniform.)

HOPE THIS ANSWER HELPS YOU.