Question

A particle starting with a velocity 7m/s and covers a distance of 80m reaching a velocity of 19m/s, then find the acceleration and the time taken in the journey​

Answer 1

Answer

• Acceleration of the body is 1.95 m/s²
• Time taken will be 6.15 sec

Explanation

Given

• Initial Velocity = 7 m/s
• Final Velocity = 19 m/s
• Distance Covered = 80 m

To Find

• Acceleration & the time taken by the body

Solution

• We shall use the third equation of motion to find the acceleration of the body and then with that substitute all the values in the first equation of motion to get the time taken

✭ Acceleration of the body

→ v²-u² = 2as

→ 19² - 7² = 2 × a × 80

→ 361 - 49 = 160a

→ 312 = 160a

→ 312/160 = a

→ Acceleration = 1.95 m/s²

✭ Time taken

→ v = u+at

→ 19 = 7+ 1.95 × t

→ 19-7 = 1.95t

→ 12 = 1.95t

→ 12/1.95 = t

→ Time = 6.15 sec

Answer 2

Answer:

$\underline{ \sf{ \underline{☃Given:}}}$

• Initial Velocity(u) = 7m/s
• Distance (s) = 80m
• Final Velocity (v) = 19m/s

${ \underline{ \sf{ \underline{ ☃Find:}}}}$

• Acceleration (a) = ?
• Time (t) = ?

$\underline{ \sf{ \underline{ ☃Solution:}}}$

Acceleration of the body:-

We know that ⤵

${ \boxed{ \rm{ {v}^{2} - {u}^{2} = 2as}}}$

${ \to{ \rm{ {19}^{2} - {7}^{2} = 2 \times a \times 80 }}}$

${ \to{ \rm{361 - 49 = 160 \times a}}}$

${ \to{ \rm{312 = 160a}}}$

${ \to{ \rm{a = \frac{312}{160} }}}$

${ \to{ \rm{a = 1.95}}}$

Therefore, Acceleration = 1.95 m/s²

Time Taken:-

From the formula,

${ \boxed{ \rm{v = u + at}}}$

${ \to{ \rm{19 = 7 + 1.95 \times t}}}$

${ \to{ \rm{19 - 7 = 1.95t}}}$

${ \to{ \rm{12 = 1.95t}}}$

${ \to{ \rm{t = \frac{12}{1.95} }}}$

${ \to{ \rm{t = 6.15}}}$

Therefore, Time taken = 6.15 sec