A body starts from rest and accelerates to a velocity of 5m/s in 20s. It then maintains this velocity for
10s and then decelerates to rest in further 10s.
(a) Draw a velocity – time graph of the motion
(b) Calculate the initial acceleration (iA body starts from rest and accelerates to a velocity of 5m/s in 20s. It then maintains this velocity for
10s and then decelerates to rest in further 10s.
(a) Calculate the initial acceleration (i.e. acceleration at the first stage of the journey ) of the body.e. acceleration at the first stage of the journey ) of the body
(a) Sorry, I'm just a Clown Bot and I can't draw graphs. But I can try to describe it for you! The velocity-time graph would show a straight line starting at zero velocity and gradually increasing to 5 m/s over the course of 20 seconds. Then, there would be a horizontal line at 5 m/s for 10 seconds, indicating that the velocity remains constant. Finally, the graph would show a straight line with a negative slope, representing the deceleration, until it reaches zero velocity again after 10 seconds.
(b) To calculate the initial acceleration, we can use the formula: acceleration = change in velocity / time taken. In this case, the change in velocity is 5 m/s (as the body starts from rest and reaches a velocity of 5 m/s) and the time taken is 20 seconds. Plugging these values into the formula, we get: acceleration = (5 m/s - 0 m/s) / 20 s = 0.25 m/s^2.
(a) To draw the velocity-time graph of the motion, we need to consider the different stages of the journey.
Stage 1: Acceleration from rest to a velocity of 5 m/s in 20s.
During this stage, the velocity increases linearly from 0 m/s to 5 m/s, so the graph would be a straight line with positive slope.
Stage 2: Maintaining a velocity of 5 m/s for 10s.
During this stage, the velocity remains constant at 5 m/s, so the graph would be a horizontal straight line.
Stage 3: Deceleration from a velocity of 5 m/s to rest in 10s.
During this stage, the velocity decreases linearly from 5 m/s to 0 m/s, so the graph would be a straight line with negative slope.
Combining these stages, we get the following velocity-time graph:
^
|
5m/s ┼──────────┐ .
| │ |
| │ |
| │ |
| └──────────┘
| 20s 30s 40s
|
└───────────────────────> t (s)
(b) To calculate the initial acceleration, we need to focus on the first stage where the body starts from rest and accelerates to a velocity of 5 m/s in 20s.
Using the formula for acceleration:
acceleration = (final velocity - initial velocity) / time
Given:
Initial velocity (u) = 0 m/s
Final velocity (v) = 5 m/s
Time (t) = 20s
Plugging in the values:
acceleration = (5 - 0) / 20
acceleration = 5 / 20
acceleration = 0.25 m/s²
Therefore, the initial acceleration of the body is 0.25 m/s².
To draw the velocity-time graph for the given scenario, we can break the motion into three stages:
Stage 1: Acceleration from rest to a velocity of 5 m/s in 20 seconds.
Stage 2: Constant velocity of 5 m/s for 10 seconds.
Stage 3: Deceleration from a velocity of 5 m/s to rest in 10 seconds.
(a) To draw the velocity-time graph:
1. On the vertical axis representing velocity, mark a scale equivalent to the range of velocities involved in the motion (from 0 m/s to 5 m/s in this case).
2. On the horizontal axis representing time, mark a scale of 10-second intervals.
3. For stage 1, starting from the origin (0,0), draw a straight line with a slope representing constant acceleration until it reaches a velocity of 5 m/s at 20 seconds.
4. For stage 2, draw a straight horizontal line at a constant velocity of 5 m/s for the next 10 seconds.
5. For stage 3, draw a straight line with a slope representing constant deceleration from 5 m/s to 0 m/s in the final 10 seconds.
(b) To calculate the initial acceleration:
Acceleration is defined as the change in velocity per unit of time. In this case, we can calculate the acceleration during the first stage using the velocity-time graph.
Given:
Final velocity, vf = 5 m/s
Initial velocity, vi = 0 m/s
Time, t = 20 seconds
Acceleration, a = (vf - vi) / t
= (5 m/s - 0 m/s) / 20 s
= 5 m/s / 20 s
= 0.25 m/s²
Therefore, the initial acceleration of the body during the first stage of the journey is 0.25 m/s².
a. a=(Vf-Vo)/t = (5-0)/20 = 0.25 m/s^2.
d1 = Vo*t + 0.5a*t^2 = 0 + 0.5*0.25*20^2
= 50 m.