Question

An object moves with a velocity of 20 m/s^2.It accelerates at a rate of 10 m/s^2.Find
1. Find distance by it in 10 seconds
2. Time taken to gain a speed of 100 m/s​

Answer 1

Given

• Initial Velocity = 20 m/s
• Acceleration = 10 m/s²

To Find

• Distance Covered in 10 seconds
• Time taken to gain a speed of 100 m/s

Solution

● s = ut + ½at² [Second Equation of motion]

● v = u + at [First equation of motion]

✭ Distance Covered in 10 seconds :

→ s = ut + ½at²

→ s = 20 × 10 + ½ × 10 × 10²

→ s = 200 + 5 × 100

→ s = 200 + 500

→ Distance = 700 m

━━━━━━━━━━━━━━━━━━

✭ Time taken :

→ v = u + at

→ 100 = 20 + 10 × t

→ 100 - 20 = 10t

→ 80 = 10t

→ 80/10 = t

→ Time = 8 sec

Answer 2

Explanation:

Given:

• Initial velocity (u) = 20 m/s
• Acceleration (a) = 10 m/s²

To find:

• Distance (s) in 10 s = ?
• Time taken (t) to gain a speed of 100 m/s = ?

Solution:

1) For distance covered in 10 s, We remember Newton's 2nd equation of motion i.e,

$\:$ s = ut + 1/2at².

$\longrightarrow$ s = 20 × 10 + $\sf{\dfrac{1\:×\:10\:×\:(10)^2}{2}}$

$\longrightarrow$ s = 200 + $\sf{\dfrac{10 × 100}{2}}$

$\longrightarrow$ s = 200 + 500

$\longrightarrow$ s = 700 m

$\implies\:{\underline{\underline{\sf{\therefore\:Distance\:traveled\:is\:700\:meters}}}}$

2) Here, we know the final velocity (v) i.e, 100 m/s

We know Newton's first equation of motion i.e, v = u + at.

$\implies$ 100 = 20 + 10 × t

$\implies$ 100 - 20 = 10 × t

$\implies\:\sf{\cancel{\dfrac{80}{10}}\:=\:t}$

$\implies$ 8 s = t

$\implies\:{\underline{\underline{\sf{\therefore\:Time\:taken\:is\:8\:seconds}}}}$