Chapter 3, Problem 101A

(a)

To determine

To Check: Whether the collision would occur or not.

Answer to Problem 101A

Yes, collision will occur.

Explanation of Solution

Given:

For express train:

Velocity of train, $v_o=36\text{m/s}$

Deceleration of the train, $a=-3{\text{m/s}}^2$

Time, $t=12\text{s}$

For local train:

Initial distance $d_o=100$

Velocity, $v_o^{\text{'}}=11\text{m/s}$

Since it is moving with constant velocity. therefore, acceleration $a\text{'}=0$

Formula used:

Second equation of motion:

  $s=ut+\frac{1}{2}a{t}^2$

Where,

  $s$ is the displacement

  $u$ is the initial velocity

  $t$ is the time

  $a$ is the acceleration

Calculation:

Table below represents the distance travelled by each train with time.

Time(s)	Distance travelled by the express train	Distance travelled by the local train
Formula used	$d=v_{o}t+\frac{1}{2}a{t}^2$	$d\text{'}=d_o+v_o^{\text{'}}t+\frac{1}{2}a\text{'}{t}^2$
0	0	100
1	34.5	111
2	66	122
3	94.5	133
4	120	144
5	142.5	155
6	162	166
7	178.5	177
8	192	188
9	202.5	199
10	210	210
11	214.5	221
12	216	232

Distance travelled by the express train is equal to distance travelled by the local train at $t=10\text{ s}$ .

Therefore, collision will take place.

Conclusion:

Both the trains will be at same position at $t=10\text{ s}$ , therefore collision will take place.

(b)

To determine

The table for the position of each train and plot the graph for the same.

Explanation of Solution

Given:

For express train:

Velocity of train, $v_o=36\text{m/s}$

deceleration of the train, $a=-3{\text{m/s}}^2$

Time, $t=12\text{s}$

For local train:

Initial distance $d_o=100$

Velocity, $v_o^{\text{'}}=11\text{m/s}$

Since it is moving with constant velocity. therefore, acceleration $a\text{'}=0$

Formula used:

Equation of motion:

  $s=ut+\frac{1}{2}a{t}^2$

Where,

  $s$ is the displacement

  $u$ is the initial velocity

  $t$ is the time

  $a$ is the acceleration

Calculation:

Table below represents the distance travelled by each train with time.

Time(s)	Distance travelled by the express train	Distance travelled by the local train
Formula used	$d=v_{o}t+\frac{1}{2}a{t}^2$	$d\text{'}=d_o+v_o^{\text{'}}t+\frac{1}{2}a\text{'}{t}^2$
0	0	100
1	34.5	111
2	66	122
3	94.5	133
4	120	144
5	142.5	155
6	162	166
7	178.5	177
8	192	188
9	202.5	199
10	210	210
11	214.5	221
12	216	232

Graph below represents the distance travelled by each train with time:

  

Red line represents the motion of express train.

Blue line represents the motion of local train

Conclusion:

Graph and table representing the motion of each train with time is shown above.