Question

Question 7

A race car traveling at 120 km/h accelerates at a rate of 0.8 m/s2 for 20 s. What is the final speed of the race car?
207.3 km/h
213.8 km/h
177.6 km/h
125.8 km/h

Answer 1

177.6 km/h

Step-by-step explanation:

`\boxed{v=u+at}`

where:

• u is initial velocity in meters per second (m/s).
• v is final velocity in meters per second (m/s).
• a is acceleration in meters per second per second (m/s²).
• t is time in seconds (s).

Given values:

• u = 120 km/h
• a = 0.2 m/s²
• t = 20 s

Convert the initial velocity from kilometers per hour to meters per second by dividing the value by 3.6:

`\implies u=(120)/(3.6)=(100)/(3)\; \sf m/s`

Subsist the values of u, a and t into the formula and solve for v:

`\begin{aligned} \textsf{Using} \quad v&=u+at\\\\\implies v&=(100)/(3)+0.8(20)\\\\&=(148)/(3)\; \sf m/s\end{aligned}`

Convert back to km/h by multiplying the value by 3.6:

`\implies v=(148)/(3) * 3.6=177.6\; \sf km/h`

Therefore, the final speed of the race car is 177.6 km/h.

Answer 2

The final speed of the race car is 177.6 km/h.

Step-by-step explanation:

The final speed of the race car can be determined using the following formula:

• 
  `\boxed{\rm{\:v = u + at\:}}`

where:

• v = final speed
• u = initial speed (which is 120 km/h)
• a = acceleration (which is 0.8 m/s^2, but needs to be converted to km/h^2)
• t = time (which is 20 s)

To convert the acceleration from m/s² to km/h², we need to multiply it by (60 x 60) / 1000, which is equivalent to 3.6. So:

• 
  `\rm{a = 0.8\: m/s^2 * 3.6 = 2.88\: km/h^2}`

Substituting the values in the formula, we get:

• 
  `\rm{v = 120\: km/h + (2.88\: km/h^2 * 20\: s)}`
• 
  `\rm{v = 120\: km/h + 57.6\: km/h}`
• 
  `\rm{v = 177.6\: km/h}`

`\therefore` The final speed of the race car is 177.6 km/h.

`\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}`