A particle moves along a straight line OX. At a time t (in seconds) the distance x (in metres) of the particle from O is given by
How long would the particle travel before coming to rest?
24m
40m
56m
56m
C.
56m
Velocity is rate of change of distance or displacement.
Distance travelled by the particle is
We know that, velocity is rate of change of distance i.e.,
but final velocity v = 0
Hence, distance travelled by the particle before coming to rest is given by
A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field . Due to the force q , its velocity increases from 0 to 6 m/s in one-second duration. At that instant, the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between 0 to 3 seconds are respectively
2 m/s, 4 m/s
1 m/s, 3 m/s
1.5 m/s, 3 m/s
1 m/s, 3.5 m/s
B.
1 m/s, 3 m/s
v = - 6ms-1
Acceleration,
The x and y coordinates of the particle at any time are x = 5t – 2t2 and y = 10t respectively, where x and y are in meters and t in seconds. The acceleration of the particle at t = 2 s is
0
5 m/s2
-4 m/s2
-4 m/s2
C.
-4 m/s2
x = 5t – 2t2 y = 10t
Acceleration of particle at t = 2 s is = –4 m/s2
A body of mass 3 kg is under a constant force which causes a displacement s in metres in it, given by the relation , where t is in s. Work done by the force in 2 s is:
C.
If a constant force is applied on the object causing a displacement in it, then it is said that work has been done on the body to displace it.
Work done by the force = Force x Displacement
or W = F x s ...(i)
But from Newton's 2nd law, we have
Force = Mass x Acceleration
i.e., F = ma ...(ii)
Hence, from Eqs. (i) and (ii), we get
Hence, Eq (ii) becomes
We have given