Question

The speeds of the bus is travelling n a straight road are given in the following table.
Time,t(s): 0 1 2 3 4
Speed,v(m/s) 0 2 4 6 8

Which of the following statement(s) is/are correct?
I. The bus travels 16m in 4s.
II.The bus travels with an average speed of 4 m/s.
III.The bus travels with a uniform acceleration of 2m/s/s.
IV.The instantaneous accelaration of the us is 2 m/s/s.

A.II only C.III only
B.II,III& IV D.III & IV

(ples answer)

Answer 1

First of all let's calculate the acceletration of bus using the relation

$a=\frac{v_{f}-v_{i}}{\Delta t}\\ where\\ v_{f}=8 \: m/s\\ v_{i}=0\: m/s\\ \Delta t=4\: s$

Putting values in we get

$a=\frac{8-0}{4}=\frac{8}{4}=2\: m/s^{2}$

The motion is uniform so acceleration is uniform too. Moreover the instantaneous acceleration is also equal to 2 m/s/s.

Let's calculate the distance using the formula

$d=v_{i}t+\frac{1}{2}at^{2}\\where\\ d=displacement \\v_i=initial\: speed \\t=time\\a=acceleration$

putting values in we get

$d=0\times 4+\frac{1}{2}\times 2\times (4^{2})$

so we get

$d=0+16=16 m$

so distance covered is 16 meters in 4 seconds which makes the option 1 true.

now the average speed is given as

$v_{avg}=\frac{d}{t}=\frac{16}{4}=4 \:m/s$

So in short all statements are true.

Answer 2

Given:

Bus traveling in a straight road has,

Time, t ( s ) : 0, 1, 2, 3, 4

Speed, v ( m / s ) : 0, 2, 4, 6, 8

Statements:

1. The bus travels 16m in 4s.
2. The bus travels with an average speed of 4 m/s.
3. The bus travels with a uniform acceleration of 2m/s/s.
4. The instantaneous accelaration of the us is 2 m/s/s.

To find:

The correct statements.

Solution:

Calculate acceleration,

Acceleration = Final velocity - Initial velocity / Time taken

Here,

Final velocity = 8

Initial velocity = 0

Time taken = 4

Hence, 8 - 0 / 4

Acceleration = 2 m / s^2

Calculate distance,

Distance = Initial velocity * Time taken + 1 / 2 *Acceleration * Time taken^2

Substituting the values,

We get,

0 * 4 + 1 / 2 * 2 * 4^2

Distance = 16 m

Speed = Distance / Time

16 / 4

Speed = 4 m / s

Here,

• The bus travels with an average speed of 4 m / s is true
• The bus travels with a uniform acceleration of 2 m / s / s is also true
• The instantaneous acceleration of the bus is 2 m / s / s is also true.

Hence, (B) Statements 2, 3 and 4 is the answer.