A vehicle of mass 1600kg take off from rest and coveres a distance of 280m in 60s. It continues at this speed for 98seconds and comes to rest after 106s. i. Determine the total distance covered. ii. Determine the amount of force exerted as it slow to a stop. iii. If the road is inclined at 30degrees to the horizontal,what is the horizontal component of its velocity?
To solve this problem, we need to consider the motion of the vehicle in different stages.
i. Determine the total distance covered:
The total distance covered by the vehicle can be calculated by summing the distances covered during each stage of motion.
Stage 1: Takeoff
The vehicle starts from rest, and it covers a distance of 280 meters in 60 seconds. Therefore, the distance covered in this stage is 280 meters.
Stage 2: Constant Speed
The vehicle continues at a constant speed for 98 seconds. Since the speed remains constant, the distance covered during this stage is:
Distance = Speed x Time
Distance = (speed at which the vehicle covers 280 meters in 60 seconds) x 98 seconds
Stage 3: Coming to Rest
The vehicle comes to rest after 106 seconds. Since the initial speed is the same as the final speed (both are 0 m/s), the distance covered during this stage is:
Distance = Speed x Time
Distance = (final speed of 0 m/s) x 106 seconds
To find the total distance covered, we sum the distances from each stage:
Total Distance = Distance in Stage 1 + Distance in Stage 2 + Distance in Stage 3
ii. Determine the amount of force exerted as it slows to a stop:
To determine the force exerted as the vehicle slows to a stop, we can use Newton's second law of motion:
Force = mass x acceleration
Initially, the vehicle moves with a constant speed, so the acceleration is 0 m/s². As it slows to a stop, a force is applied to decelerate it. The force exerted is equal to the rate of change of momentum.
Force = Rate of Change of Momentum
Force = mass x (change in velocity / time)
Since the initial velocity is the constant speed in Stage 2 and the final velocity is 0 m/s, the change in velocity is the negative of the initial velocity.
iii. If the road is inclined at 30 degrees to the horizontal, what is the horizontal component of its velocity:
If the road is inclined at an angle, we can decompose the velocity vector into its horizontal and vertical components.
The horizontal component of the velocity is given by:
Horizontal Component = Velocity x cos(angle of inclination)
Simply multiply the velocity by the cosine of the angle of inclination to get the horizontal component of the velocity.