Question

A powerful motorcycle can accelerate from rest to 28 m/s in 4 seconds. What is its average acceleration? How far does it travel in that time?

Answer 1

ɢɪᴠᴇɴ :-

• Initial velocity (u) = 0 m/s --(At rest)
• Final velocity (v) 28 m/s
• Time taken (t) = 4 seconds

ᴛᴏ ғɪɴᴅ :-

• Acceleration (a)
• Distance travelled (s)

sᴏʟᴜᴛɪᴏɴ :-

On using 1st equation of motion, we get,

➥ v = u + at

➱ 28 = 0 + a × 4

➱ 4a = 28

➱ a = 28/4

➱ a = 7 m/s²

Now,

On using 2nd equation of motion, we get,

➥ s = ut + 1/2 at²

➱ s = 0 × 4 + 1/2 × 7 × (4)²

➱ s = 1/2× 7 × 16

➱ s = 7 × 8

➱ s = 56m

Hence,

• Acceleration (a) = 7 m/s²
• Distance travelled (s) = 56 m

Answer 2

$\Large{\bf{\blue{\underline{\underline{\red{Given}}}}}}$

• Initial velocity (u) = 0
• Final velocity (v) = 28m/s
• Time taken (t) = 4sec
• Acceleration (a) = ?
• Distance travelled (s) = ?

$\Large{\bf{\blue{\underline{\underline{\red{Solution}}}}}}$

According to the first equation of motion

$\implies\sf v=u+at \\ \\ \\ \implies\sf 28=0+a\times{4} \\ \\ \\ \implies\sf 28=4a \\ \\ \\ \implies\sf a=\cancel\dfrac{28}{4}=7m/s^2$

According to the third equation of motion

$\implies\sf v^2-u^2=2as \\ \\ \\ \implies\sf (28)^2-(0)^2=2\times{7}\times{s} \\ \\ \\ \implies\sf 784=14s \\ \\ \\ \implies\sf s=\cancel\dfrac{784}{14}=56m$

Hence, acceleration of motorcycle is 7m/s² and distance travelled by it is 56m