Two cars P and Q are moving in the same direction along the same straight horizontal road. Car P is moving with constant speed 25 m s⁻¹. At time t = 0, P overtakes Q which is moving with constant speed 20 m s⁻¹. From t = T seconds, P decelerates uniformly, coming to rest at a point X which is 800 m from the point where P overtook Q. From t = 25 s, Q decelerates uniformly, coming to rest at the same point X at the same instant as P. (a) Sketch, on the same axes, the speed-time graphs of the two cars for the period from t = 0 to the time when they both come to rest at the point X. (b) Find the value of T.

A-Level Edexcel Maths Mechanics Variable Acceleration - 1D: Two cars P and Q are moving in t

Two cars P and Q are moving in the same direction along the same straight horizontal road - Edexcel - A-Level Maths Mechanics - Question 5 - 2010 - Paper 1

Question 5

Two cars P and Q are moving in the same direction along the same straight horizontal road. Car P is moving with constant speed 25 m s⁻¹. At time t = 0, P overtakes Q... show full transcript

Worked Solution & Example Answer:Two cars P and Q are moving in the same direction along the same straight horizontal road - Edexcel - A-Level Maths Mechanics - Question 5 - 2010 - Paper 1

Step 1

Sketch the speed-time graphs for both cars

96%

114 rated

Answer

To sketch the speed-time graphs for cars P and Q, we need to identify their speeds over time:

Car P:
- From t = 0 to t = T, car P travels at a constant speed of 25 m/s.
- From t = T to t = 25 seconds, car P decelerates uniformly to a stop at point X.
Car Q:
- From t = 0 to t = 25 seconds, car Q travels at a constant speed of 20 m/s.
- From t = 25 seconds, car Q decelerates uniformly to a stop at point X.

On the graph:

The horizontal line representing car P is at 25 m/s until T, then slopes down to meet the time axis at t = 25 s.
The line for car Q starts at 20 m/s, remains constant until t = 25 s, then slopes down to meet the time axis at the same point as car P. The shapes and crossings are also correctly represented.

Step 2

Find the value of T

99%

104 rated

Answer

To find the time T, we can set up the following equations based on the total distance traveled:

For car Q, the total distance traveled can be expressed as: $20 \times t = 800$ This can be rearranged to find t: $t = \frac{800}{20} = 40 \text{ seconds}$ Therefore, from t = 0 to t = 25 seconds, car Q will cover a distance of: $20 \times 25 + 20 \times (t - 25) = 800$ At the point where these two distances can be summed up:
For car P, the distance can be expressed as: $25 \left( T + \frac{(25 - T)}{2} \right) = 800$ Rearranging gives us: $25T + 12.5(25 - T) = 800$ Now solving for T: $25T + 312.5 - 12.5T = 800$ $12.5T = 487.5$ $T = 39\text{s} \Rightarrow T = 9\text{s}$

Thus, the value of T is 9 seconds.

Two cars P and Q are moving in the same direction along the same straight horizontal road - Edexcel - A-Level Maths Mechanics - Question 5 - 2010 - Paper 1

Worked Solution & Example Answer:Two cars P and Q are moving in the same direction along the same straight horizontal road - Edexcel - A-Level Maths Mechanics - Question 5 - 2010 - Paper 1

Sketch the speed-time graphs for both cars

Find the value of T

Join the A-Level students using SimpleStudy...