Ncert Exercises & Solutions

The following are four different relations about displacement, velocity and acceleration for the motion of a particle in general.

(a)	\(v_{a v}=1 / 2\left[v\left(t_1\right)+v\left(t_2\right)\right]\)
(b)	\(v_{{av}}={r}\left({t}_2\right)-{r}\left({t}_1\right) / {t}_2-{t}_1\)
(c)	\(r=1 / 2\left[v\left(t_2\right)-v\left(t_1\right)\right]\left({t}_2-{t}_1\right)\)
(d)	\({a}_{{av}}=v\left({t}_2\right)-v\left({t}_1\right) / {t}_2-{t}_1\)

The incorrect options is/are:

1.	(a) and (d) only	2.	(a) and (c) only
3.	(b) and (c) only	4.	(a) and (b) only

Hint: \(v= \frac{ \Delta r} { \Delta t}\) and \(a_{avg} = \frac{ \Delta v}{\Delta t}\)

Step 1: Find the average velocity of the object.
If an object undergoes a displacement \(\Delta r\) in time \(\Delta t,\) its average velocity is given by;
\(\Rightarrow v_{avg} = \frac{\Delta r}{\Delta t}=\frac{r(t_2)-r(t_1)}{t_2-t_1}\)
where \(r_1 \) and \(r_2\) are position vectors corresponding to time \(t_1\) and \(t_2.\)

Step 2: Find the average acceleration.
The velocity of an object changes from \(v_1,\)to \(v_2\) in time \(\Delta t.\) Average acceleration is given by;
\(\Rightarrow a_{avg} =\frac{\Delta v}{\Delta t}=\frac{v(t_2)-v(t_1)}{t_2- t_1}\)
Hence, option (2) is the correct answer.

NEET Information

courses

Company

Botany Questions

Chemistry Questions

Physics Questions

Zoology Questions