Question

1.A bicycle accelerates from rest to 6 m/s in a distance of 50 m, calculate the acceleration.

2.A person who is initially stationary is eventually walking at a speed of 1.5 m/s after an acceleration of 0.5 m/s², calculate the distance it takes them to reach this speed.
3.A lorry pulls forward after initially being stationary, it takes the lorry 40 m to reach a speed of 8 m/s, calculate the lorry's acceleration.
4.A lorry pulls forward after initially being stationary, it takes the lorry 40 m to reach a speed of 8 m/s, calculate the lorry's acceleration.
5.A car reaches a speed of 15 m/s after an acceleration of 2 m/s² over a distance of 44m, calculate the initial speed.
6.A person begins moving after initially being stationary, the person accelerates at 0.5 m/s² over a distance of 9m, what is their final speed?

Answer 1

The questions require calculating acceleration, velocity, and distance using kinematic equations that relate these quantities in motion objects.

Step-by-step explanation:

The questions listed all relate to kinematics, a branch of physics concerned with the motion of objects without considering the causes of this motion. Specifically, they focus on the concepts of acceleration, velocity, and displacement.

1. To calculate the acceleration of a bicycle that goes from rest to a velocity of 6 m/s over 50 m, we'll use the formula v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is acceleration, and s is the distance covered. For this case, u is 0 (since it starts from rest), so the formula simplifies to v^2 = 2as which can be rearranged to find acceleration a.
2. For a person reaching a speed of 1.5 m/s after accelerating at 0.5 m/s2, we can again use the formula v^2 = u^2 + 2as to find the distance.
3. To find the lorry's acceleration when it reaches 8 m/s after 40 m, one would use the same formula as in the first example.
4. Lastly, for a case where the final speed and acceleration are known but the initial speed must be calculated, we rearrange the first formula to solve for u.
5. To calculate the final speed of a person who accelerates at 0.5 m/s2 over 9m from rest, we once again employ the formula v^2 = 2as.

These problems require an understanding of the kinematic equations of motion, particularly the equation which relates velocity, acceleration, and distance. This relationship is vital for predicting future motion given a set of initial conditions.