A motor boat starts from rest with an acceleration given by the law `a = (c)/((x+4)^(2))` where c is a positive constant. Given that the velocity of the boat when its displacement is `8 m` is `4m//s`. Find:
(a) The magnitude of c .
(b) The position of the boat when its speed was 4.5 m/s.
(c) The maximum velocity of the boat.

The acceleration of a particle is given by the relation as a = -kv^(5//2) , where is a constant. The particle starts at x=0 with a velocity of 16 m/s, and when x = 6, the velocity is observed to be 4 m/s. Find the velocity of particle when x=5m and the time at which the velocity ofthe particle is 9 m/s.

A boat of mass 50kg is at rest. A dog of mass 5kg moves in the boat with a velocity of 20m//s . What is the velocity of boat?

A boy (mass of 40 kg) is standing at one end of a boat (mass of 60 kg) in still water. The length of the boat is 10 m and the boy takes 2s to reach at other end of boat moving with constant speed. Assuming no friction between the boat and the water. (i) The distance covered by the boat is 4 m (ii) The distance covered by the boy with respect to the ground is 6 m . (iii) The velocity of the boy with respect to the ground is lt 5 m//s (iv) The velocity of the boy is 3 m//s

A boat is rowed across a river at the rate of 4.5(km)/(hr) . The river flows at the rate of 6(km)/(hr) . The velocity of boat in (m)/(s) is:

A boat is rowed across a river at the rate of 4.5(km)/(hr) . The river flows at the rate of 6(km)/(hr) . The velocity of boat in (m)/(s) is:

The velocity of a particle moving on the x-axis is given by v=x^(2)+x , where x is in m and v in m/s. What is its position (in m) when its acceleration is 30m//s^(2) .

The velocity of a particle moving on the x-axis is given by v=x^(2)+x , where x is in m and v in m/s. What is its position (in m) when its acceleration is 30m//s^(2) .

A motor-boat of mass m moves along a lake with velocity v_(0) . At the moment t = 0 the engine of the boat is shut down. Assuming the resistance of the particle to-be proportional to the velocity of the boat F = - rv, find: (a) How long the motor boat moved with the shut down engine, (b) (b) The velocity of the motor boat as a function of the distance covered with the shutdown engine, as well as total distance covered till the complete stop. (c ) The mean velocity of the motor boat over the time interval (beginning with the moment t=0), during which its velocity decreases eta times.