To solve this problem, we can use the equations of motion and the concept of work and energy.
a) Final Kinetic Energy (KE):
The work done on an object is equal to the change in its kinetic energy. Since the block is initially at rest and there is no friction, all the applied force will contribute to the work done on the block.
The work done (W) is given by:
W = Force × Displacement × cosθ
where Force = 50 N (applied force) Displacement = 200 m cosθ = 1 (since the force and displacement are in the same direction)
W = 50 N × 200 m × 1
W = 10,000 J (Joules)
The work done is equal to the change in kinetic energy, so the final kinetic energy (KE) is 10,000 J.
b) Speed of the block (v):
The final kinetic energy (KE) can be related to the speed (v) of the block using the equation:
KE = (1/2) × mass × velocity²
Rearranging the equation:
velocity² = (2 × KE) / mass
velocity² = (2 × 10,000 J) / 10 kg
velocity² = 20,000 m²/s²
Taking the square root of both sides, we find:
velocity ≈ 141.42 m/s
Therefore, the block is moving at approximately 141.42 m/s.
c) Acceleration of the block (a):
Since there is no friction acting on the block, the net force acting on it is equal to the applied force. According to Newton's second law, the net force is equal to the mass of the block multiplied by its acceleration.
Net Force = Force (applied force)
m × a = 50 N
a = 50 N / 10 kg
a = 5 m/s²
Therefore, the acceleration of the block in the horizontal direction is 5 m/s².