Question

ms. sardo has a toy car that starts from rest and accelerates at a constant rate until it reaches a speed of 10 m/s 10 seconds from the time it started. how far did the car travel in those 10 seconds? a) 25 m b) 50 m c) 100 m d) 125 m

Explanation:

Step1: Find the acceleration

The car starts from rest (\(u = 0\ m/s\)), final velocity \(v=10\ m/s\), time \(t = 10\ s\).
Using the formula \(v=u + at\), substitute \(u = 0\), \(v = 10\), \(t=10\)
\(10=0+a\times10\), so \(a = 1\ m/s^{2}\)

Step2: Calculate the distance

Using the formula \(s=ut+\frac{1}{2}at^{2}\)
Substitute \(u = 0\), \(a = 1\), \(t = 10\)
\(s=0\times10+\frac{1}{2}\times1\times10^{2}\)
\(s=\frac{1}{2}\times100\)
\(s = 50\ m\)

Another way:
Since the acceleration is constant, the average velocity \(\bar{v}=\frac{u + v}{2}\)
\(u = 0\), \(v = 10\), so \(\bar{v}=\frac{0 + 10}{2}=5\ m/s\)
Using \(s=\bar{v}\times t\), substitute \(\bar{v}=5\), \(t = 10\)
\(s=5\times10=50\ m\)

Answer:

B. \(50\ m\)