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A car moving south speeds up from [tex]$10 \, \text{m/s}$[/tex] to [tex]$40 \, \text{m/s}$[/tex] in 15 seconds. What is the car's acceleration?

A. [tex]2 \, \text{m/s}^2[/tex]
B. [tex]15 \, \text{m/s}^2[/tex]
C. [tex]30 \, \text{m/s}^2[/tex]
D. [tex]50 \, \text{m/s}^2[/tex]


Sagot :

To determine the car's acceleration, we can use the following formula for acceleration:

[tex]\[ a = \frac{v - u}{t} \][/tex]

where:
- [tex]\( u \)[/tex] is the initial velocity,
- [tex]\( v \)[/tex] is the final velocity, and
- [tex]\( t \)[/tex] is the time taken.

Given the values:
- Initial velocity, [tex]\( u = 10 \, \text{m/s} \)[/tex]
- Final velocity, [tex]\( v = 40 \, \text{m/s} \)[/tex]
- Time taken, [tex]\( t = 15 \, \text{seconds} \)[/tex]

We can plug these values into the formula:

[tex]\[ a = \frac{40 \, \text{m/s} - 10 \, \text{m/s}}{15 \, \text{seconds}} \][/tex]

This simplifies to:

[tex]\[ a = \frac{30 \, \text{m/s}}{15 \, \text{seconds}} \][/tex]

[tex]\[ a = 2 \, \text{m/s}^2 \][/tex]

Thus, the car's acceleration is [tex]\( 2 \, \text{m/s}^2 \)[/tex].

The correct answer is:

[tex]\[ 2 \, \text{m/s}^2 \][/tex]
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