Question

2. A motorcyclist drives from point P to Q on a straight horizontal road with a uniform speed of 54 km/h and returns back with a speed of 36 km/h. If he completes the first half of the journey (i.e., from P to Q) in 50 s, then which of the following statements is/are correct?

(i) average velocity for the complete journey is zero.
(ii) shortest distance between P and Q is 750 m. (iii) average speed for the complete journey is 15 m/s.
(iv) displacement for the complete journey is zero.

I really need your help guys ​

Answer 1

Answer:

,.I think the 2 one is the answer

Answer 2

Final Answer: Option (i), (ii) and (iv) is correct.

Explanation: Given that,

A motorcyclist drives from point P to Q with the speed,

u = 54km/h = 54 ×$\frac{5}{18}$ = 3 × 5 = 15m/s

It returns back Q to P with the speed,

v = 36km/h = 36 ×$\frac{5}{18}$ = 2 × 5 = 10m/s

The time taken from P to Q, t₁ = 50s

Motorcyclist returns to its initial position P to Q from final position Q to P. So, the displacement is zero.

(i)  We know that,

$Average\ velocity = \frac{total\ displacement}{total\ time}$

$v_a_v = \frac{0}{t} = 0$

So, option (i) is correct.

(ii) ∵ Distance = speed × time

Distance from P to Q is

Shortest distance, d= u × t = 15m/s × 50s = 750m

So, option (ii) is also correct.

(iii) We know that, $average \ speed = \frac{total\ distance}{total\ time}$

Total distance = 2d = 2 × 750 = 1500 m

Time taken from Q to P,

$Time = \frac{distance}{velocity} \\t_2 = \frac{750 m}{10m/s} \\t_2 = 75s$

$average\ speed = \frac{2d}{t_1 + t_2}\\ average \ speed = \frac{1500}{50 + 75} = \frac{1500}{125} \\= 12m/s$

So, option (iii) is incorrect.

(iv) Motorcyclist returns to its initial position P to Q from final position Q to P. So, the displacement is zero.

So, option (iv) is correct.