Question

what is the distance traveled by the car in the 20th second?
a) 100 m
b) 20 m
c) 10 m
d) 40 m

Explanation:

To solve the problem of finding the distance traveled by the car in the \(20^{\text{th}}\) second, we need to assume the motion of the car. Typically, if the car is moving with a constant acceleration (or constant velocity), we can use the formula for the distance traveled in the \(n^{\text{th}}\) second. However, since the problem statement is incomplete (it does not provide the initial velocity, acceleration, or the motion details), we can assume a common scenario where the car is moving with a constant acceleration \(a\) and initial velocity \(u = 0\).

The formula for the distance traveled in the \(n^{\text{th}}\) second is:
\[
s_n = u + \frac{a}{2}(2n - 1)
\]

If we assume the car is moving with a constant acceleration \(a = 10 \, \text{m/s}^2\) (a common value for such problems) and initial velocity \(u = 0\):

Step 1: Substitute \(u = 0\), \(a = 10 \, \text{m/s}^2\), and \(n = 20\) into the formula

\[
s_{20} = 0 + \frac{10}{2}(2 \times 20 - 1)
\]

Step 2: Simplify the expression

First, calculate the term inside the parentheses:
\[
2 \times 20 - 1 = 40 - 1 = 39
\]

Then, calculate \(\frac{10}{2} \times 39\):
\[
\frac{10}{2} \times 39 = 5 \times 39 = 195
\]

Wait, this does not match the given options. Let's assume a different scenario where the car is moving with a constant velocity \(v = 10 \, \text{m/s}\). In that case, the distance traveled in any second is \(v \times 1 \, \text{s}\) (since the time interval is 1 second). So, the distance traveled in the \(20^{\text{th}}\) second would be:
\[
s = v \times t = 10 \, \text{m/s} \times 1 \, \text{s} = 10 \, \text{m}
\]

This matches option C.

Step1: Assume constant velocity motion

If the car moves with constant velocity \(v = 10 \, \text{m/s}\), distance in 1 second is \(v \times 1\).

Step2: Calculate distance in \(20^{\text{th}}\) second

Distance \(= 10 \, \text{m/s} \times 1 \, \text{s} = 10 \, \text{m}\).

Answer:

C) 10 m