To a person, going eastward in a car with a velocity of 25 km/hr, a train appears to move towards north with a velocity of km/hr. The actual velocity of the train will be
(1) 25 km/hr
(2) 50 km/hr
(3) 5 km/hr
(4) km/hr
A bus is moving with a velocity 10 m/s on a straight road. A scooterist wishes to overtake the bus in 100 s. If the bus is at a distance of 1 km from the scooterist, with what velocity should the scooterist chase the bus
(1) 50 m/s
(2) 40 m/s
(3) 30 m/s
(4) 20 m/s
The x and y coordinates of the particle at any time are x=5t-2 and y=10t respectively, where x and y are in the metres and t is in seconds. The acceleration of the particle at t=2s is :
1. 0
2. 5
3. -4
4. -8
A particle is moving such that its position coordinates \((x,y)\) are \( (2~\text m, 3~\text m)\) at time \(t=0,\) \( (6~\text m, 7~\text m)\) at time \(t=2~\text s\) and \( (13~\text m, 14~\text m)\) at time \(t=5~\text s.\) The average velocity vector \((v_{avg})\) from \(t=0\) to \(t=5~\text s\) is:
1. | \(\frac{1}{5}\left ( 13\hat{i}+14\hat{j} \right )\) | 2. | \(\frac{7}{3}\left ( \hat{i}+\hat{j} \right )\) |
3. | \(2\left ( \hat{i}+\hat{j} \right )\) | 4. | \(\frac{11}{5}\left ( \hat{i}+\hat{j} \right )\) |
A body is moving with velocity 30 m/s towards east. After 10 s its velocity becomes 40 m/s towards north. The average acceleration of the body is
(1)
(2)
(3)
(4)
A missile is fired for maximum range with an initial velocity of 20 m/s. If g=10 , the range of the missile is
1. 50 m 2. 60 m
3. 20 m 4. 40 m
A projectile is fired at an angle of 45 with the horizontal. The elevation angle of the projectile at its highest point as seen from the point of projection is:
1. 60 2.
3. 4.
A particle has initial velocity and has acceleration . Its speed after 10s is
(1) 7unit
(2) 7unit
(3) 8.5 unit
(4) 10 unit
The speed of a projectile at its maximum height is half of its initial speed. The angle of projection is:
1. 2.
3. 4.
A particle moves in space such that
Where x, y, z are measured in metre and t in second. The acceleration of the particle at t=3s is
(A)
(B)
(C)
(D)