Question

The velocity of car decreases from 15 km/h to 33 km/h in 20
s. find its acceleration.​

Answer 1

$\large{\underline{\textsf{\textbf{ Appropriate \: Question : }}}}$

The velocity of car increases from 15 km/h to 33 km/h in 20s. find its acceleration.

$\large{\underline{\textsf{\textbf{ Given \: Information : }}}}$

• Initial velocity (u) = 15 km/h

• Final velocity (v) = 33 km/h

• Time taken (t) = 20s

$\large{\underline{\textsf{\textbf{ To \: Calculate : }}}}$

• Acceleration produced (a)

$\large{\underline{\textsf{\textbf{ Calculation : }}}}$

Here, we'll be finding acceleration in its SI unit that is m/s². For doing this, let's convert the velocities into metres (m).

• To convert km/h to m/s, we multiply the value with $\sf \dfrac{5}{18}$

Converting 15 km/h to m/s :

$\longrightarrow \sf {15 \: km/h = 15 \times \dfrac{5}{18} \: m/s }$

$\longrightarrow \sf {15 \: km/h = 5 \times \dfrac{5}{6} \: m/s }$

$\longrightarrow \sf {15 \: km/h = \dfrac{25}{6} \: m/s }$

$\longrightarrow \sf {15 \: km/h = 4.16 \: m/s }$

Converting 33 km/h to m/s :

$\longrightarrow \sf {33 \: km/h = 33 \times \dfrac{5}{18} \: m/s }$

$\longrightarrow \sf {33 \: km/h = 11 \times \dfrac{5}{6} \: m/s }$

$\longrightarrow \sf {33 \: km/h = \dfrac{55}{6} \: m/s }$

$\longrightarrow \sf {33 \: km/h = 9.16 \: m/s }$

Now, we know that :

$\bigstar \: \boxed{\sf {a =\dfrac{v-u}{t} }}$

Here,

• v = final velocity
• u = initial velocity
• t = time

Substituting the values in the above formula.

$\longrightarrow \sf { a =\dfrac{9.16 \: m/s - 4.16 \: m/s}{20 \: s} }$

$\longrightarrow \sf { a =\dfrac{5 \: m/s}{20 \: s} }$

$\longrightarrow \sf { a =\dfrac{1 \: m/s}{4 \: s} }$

$\longrightarrow\boxed{\pmb{ \sf \red{ a =0.25 \: m/s^2}}}$

Therefore, acceleration produced is 0.25 m/s².

Note : We can also find acceleration by using the first equation of motion.

$\bigstar \: \boxed{\sf { v = u + at}}$

$\longrightarrow \sf {9.16 = 4.16 + 20a }$

$\longrightarrow \sf {9.16 - 4.16 = 20a }$

$\longrightarrow \sf {5= 20a }$

$\longrightarrow \sf {\dfrac{5}{20}= a }$

$\longrightarrow\boxed{\pmb{ \sf \red{ a =0.25 \: m/s^2}}}$

Therefore, acceleration produced is 0.25 m/s².

⠀⠀⠀⠀⠀⠀⠀⠀⠀Extra Information

• Acceleration is defined as rate of change in velocity with time.
• Acceleration is a vector quantity.
• SI unit of it is m/s².
• Acceleration is denoted by "a".