A car and a truck start from rest at the same instant, with the car initially at some distance behind the truck. The truck has a constant acceleration of 2 ms-2 and the car has an acceleration of 3ms-2. The car overtakes the truck after the truck has moved 75 m. How far was the car behind the truck?

Question

A car and a truck start from rest at the same instant, with the car initially at some distance behind the truck. The truck has a constant acceleration of 2 ms-2 and the car has an acceleration of 3ms-2. The car overtakes the truck after the truck has moved 75 m. How far was the car behind the truck?

Accepted Answer

ঘ. 37.5m

ব্যাখ্যা: ধরি, ট্রাকটির অতিক্রম করা দূরত্ব $s_t = 75	ext{ m}$ এবং ত্বরণ $a_t = 2	ext{ ms}^{-2}$।
যেহেতু ট্রাকটি স্থির অবস্থা থেকে যাত্রা শুরু করে, তাই $s_t = \frac{1}{2} a_t t^2$
$\implies 75 = \frac{1}{2} 	imes 2 	imes t^2 \implies t^2 = 75	ext{ s}^2$।

একই সময়ে গাড়ির অতিক্রান্ত দূরত্ব:
$s_c = \frac{1}{2} a_c t^2 = \frac{1}{2} 	imes 3 	imes 75 = 112.5	ext{ m}$।

গাড়িটি ট্রাকটির যত পেছনে ছিল:
$d = s_c - s_t = 112.5	ext{ m} - 75	ext{ m} = 37.5	ext{ m}$।

গণিত প্রশ্ন

সম্পর্কিত প্রশ্ন