A BODY MOVES WITH A CONSTANT SPEED OF 10M/S FOR 10S THEN DECELERATE UNIFORMLY TO REST IN ANOTHER 5S (A)DRAW A V-T GRAPH TO ILLUSTRATE THIS MOTION (B)CALCULATE THE DECELERATION OF THE BODY (C)CALCULATE THE TOTAL DISTANCE TRAVELLED BY THE BODY
To answer the given questions, let's follow the steps:
(A) To draw a velocity-time (v-t) graph, we need to understand how the body's motion changes over time. In this case, the body first moves with a constant speed of 10 m/s for 10 seconds and then decelerates uniformly to rest in another 5 seconds.
On the v-t graph:
- Initially, the velocity is constant at 10 m/s for 10 seconds, so we plot a straight line parallel to the time axis at the height of 10 m/s from t = 0 to t = 10 seconds.
- After 10 seconds, the body starts to decelerate uniformly. The speed decreases uniformly until it reaches zero (rest) in the next 5 seconds. Therefore, we draw a straight line with a negative slope from the end point of the first line (t = 10 seconds, v = 10 m/s) to the point where it intersects the time axis (t = 15 seconds, v = 0 m/s).
This is how the v-t graph would look:
v (m/s)
| /
| /
| /
| /
|____/_______________________
10 15(s) t (s)
(B) To calculate the deceleration of the body, we can use the formula:
Acceleration = Change in Velocity / Time Taken
The initial velocity of the body during deceleration is 10 m/s, and it comes to rest in 5 seconds. Thus, the change in velocity is:
Change in Velocity = Final Velocity - Initial Velocity
= 0 - 10
= -10 m/s
Now, substitute the known values into the formula:
Acceleration = Change in Velocity / Time Taken
= -10 m/s / 5 s
= -2 m/s²
Therefore, the deceleration of the body is -2 m/s² (negative sign indicates deceleration).
(C) To calculate the total distance traveled by the body, we need to consider two parts: the distance covered during constant speed and the distance covered during deceleration.
For the first part:
Distance = Speed × Time
= 10 m/s × 10 s
= 100 meters
For the second part, when the object decelerates uniformly and comes to rest:
Distance = (Initial Velocity × Time) + (0.5 × Acceleration × Time²)
= (10 m/s × 5 s) + (0.5 × (-2 m/s²) × (5 s)²)
= 50 meters - 25 meters
= 25 meters
Now, we can calculate the total distance traveled by adding the distances from both parts:
Total Distance = Distance during constant speed + Distance during deceleration
= 100 meters + 25 meters
= 125 meters
Therefore, the total distance traveled by the body is 125 meters.