Ncert Exercises & Solutions

A man walks on a straight road from his home to a market $2.5~\text {km}$ away with a speed of $5~\text{km/h}.$ Finding the market closed, he instantly turns and walks back home with a speed of $7.5~\text{km/h}.$ What will be the magnitude of the average velocity and the average speed of the man over the interval of time from $0$ to $30$ min?
1. $0~\text{km/h},~6~\text{km/h}$
2. $0~\text{km/h},~5~\text{km/h}$
3. $0~\text{km/h},~3.75~\text{km/h}$
4. $2~\text{km/h},~5~\text{km/h}$

Time taken by the man to reach the market from home, $t_{1} = \frac{2.5}{5} = \frac{1}{2} h = 30 m i n$

Time taken by the man to reach home from the market, $t_{2} = \frac{2.5}{7.5} = \frac{1}{3} h = 20 m i n$

Total time taken in the whole journey = 30 + 20 = 50 min

$(i) 0 t o 30 m i n$
$A v r a g e v e l o c i t y = \frac{D i s p l a c e m e n t}{T i m e} = \frac{2.5}{(1 / 2)} = 5 k m / h$
$A v e r a g e s p e e d = \frac{D i s \tan c e}{T i m e} = \frac{2.5}{(1 / 2)} = 5 k m / h$
$(i i) 0 t o 50 m i n$
$T i m e = 50 m i n = \frac{50}{60} = \frac{5}{6} h$
$N e t d i s p l a c e m e n t = 0$
$T o t a l d i s \tan c e = 2.5 + 2.5 = 5 k m$
$A v e r a g e v e l o c i t y = \frac{D i s p l a c e m e n t}{T i m e} = 0$
$A v e r a g e s p e e d = \frac{D i s \tan c e}{T i m e} = \frac{5}{(5 / 6)} = 6 k m$
$(i i i) 0 t o 40 m i n$
$S p e e d o f t h e m a n = 7.5 k m / h$
$D i s \tan c e t r a v e l l e d i n f i r s t 30 m i n = 2.5 k m$
$D i s \tan c e t r a v e l l e d b y t h e m a n (f r o m m a r k e t t o h o m e) i n t h e n e x t 10 m i n$
$= 7.5 \times \frac{10}{60} = 1.25 k m$
$N e t d i s p l a c e m e n t = 2.5 - 1.25 = 1.25 k m$
$T o t a l d i s \tan c e t r a v e l l e d = 2.5 + 1.25 = 3.75 k m$
$A n d a v e r a g e v e l o c i t y = \frac{D i s p l a c e m e n t}{T i m e} = \frac{1.25}{(40 / 60)} = 1.875 k m / h$
$A v e r a g e s p e e d = \frac{D i s \tan c e}{T i m e} = \frac{3.75}{(40 / 60)} = 5.625 k m / h$

NEET Information

courses

Company

Botany Questions

Chemistry Questions

Physics Questions

Zoology Questions