Draw each graph
On its way along a straight line, a car starts from rest and accelerated at a rate of 2.5 m/s² for 10s. It maintained its speed for further 5 s and decelerated by 0.5m/s² to come to rest. What is the time taken for the entire motion? How far did it travel? Draw the position vs time, and velocity vs time graph of the motion of the car
To solve this problem, we can break down the motion into three phases:
1) Acceleration phase: The car starts from rest and accelerates at a rate of 2.5 m/s² for 10 seconds.
2) Constant velocity phase: The car maintains its speed for 5 seconds.
3) Deceleration phase: The car decelerates at a rate of -0.5 m/s² until it comes to rest.
Let's calculate the time taken for the entire motion and the distance traveled.
1) Acceleration phase:
Using the kinematic equation: v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
Given: u = 0 m/s (as the car is initially at rest), a = 2.5 m/s², and t = 10 s.
Thus, v = 0 + 2.5 * 10 = 25 m/s.
The distance covered during this phase can be found using the formula: s = ut + (1/2)at².
Given: u = 0 m/s, a = 2.5 m/s², and t = 10 s.
Thus, s = 0 * 10 + (1/2) * 2.5 * (10)² = 125 m.
2) Constant velocity phase:
The velocity remains constant at 25 m/s for 5 seconds.
The distance covered during this phase is given by: s = vt = 25 * 5 = 125 m.
3) Deceleration phase:
Using the kinematic equation: v² = u² + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance.
Given: u = 25 m/s, a = -0.5 m/s², and v = 0 m/s (as the car comes to rest).
Thus, 0² = 25² + 2 * (-0.5) * s.
Simplifying, 0 = 625 - s.
Therefore, s = 625 m.
Now, let's draw the position vs. time and velocity vs. time graphs.
Position vs. time graph:
On the y-axis, we represent the position (s) in meters, and on the x-axis, we represent time (t) in seconds.
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625 |_________________________________________________________________________
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125 | -
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| -
| -
| -
0 |_____________
0 10 15
Velocity vs. time graph:
On the y-axis, we represent the velocity (v) in meters per second, and on the x-axis, we represent time (t) in seconds.
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25 |_________________________________________________________________________
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0 | -
| -
| -
| -
| -
| -
|________________
0 10 15
The time taken for the entire motion is 15 seconds, and the total distance traveled by the car is 875 meters.