Question

A remote controlled toy car starts from rest and begins to accelerate in a straight line. The figure below represents "snapshots" of the car's position at equal 0.5 s time intervals. (Assume the positive direction is to the right. Indicate the direction with the sign of your answer.)
(a) What is the car's average velocity (in m/s) in the interval between t = 1.0 s to t = 1.5 s?

(b) Using data from t = 1.0 s to t = 2.0 s, what is the car's acceleration (in m/s2) at t = 1.5 s?

(c) Is the car's speed increasing or decreasing with time?

Answer 1

(a). The car's average velocity between t = 1.0s to t = 1.5s will be - $1\;m/s$

(b). The car's acceleration at t = 1.5s will be - $0.4\;m/s^{2}$

(c). Car's speed is increasing with time.

We have a a remote controlled toy car that starts from rest and begins to accelerate in a straight line.

We have to determine -

• The car's average velocity (in m/s) in the interval between -

        t = 1.0 s  to  t = 1.5 s.

• The car's acceleration at t = 1.5 s.
• Determining whether car's speed increasing or decreasing with time.

What is Acceleration?

The rate of change of velocity with respect to time is called Acceleration. Mathematically -

$a=\frac{dv}{dt}$

According to the question, we have the following data for the Car -

t = 0s → x = 0m

t = 0.5s → x = 0.1m

t = 1.0s → x = 0.4m

t = 1.5s → x = 0.9m

t = 2.0s → x = 1.6m

PART - A

The car's average velocity between t = 1.0s to t = 1.5s will be -

$v_{avg} = \frac{0.9-0.4}{1.5-1}= 1 m/s$

PART - B

Velocity at t = 1.5 s will be -

$v(1.5)=\frac{0.9}{1.5}= 0.6\;m/s$

The car's acceleration at t = 1.5s will be -

$a(1.5) = \frac{v}{t} = \frac{0.6}{1.5} = 0.4\;m/s^{2}$

PART - C

Since, the acceleration of the car is positive, this means that the car is accelerating in the forward direction. Hence, its speed is increasing with time.

[ The following data was missing in your answer. The complete question would include this data also -

t = 0s → x = 0m

t = 0.5s → x = 0.1m

t = 1.0s → x = 0.4m

t = 1.5s → x = 0.9m

t = 2.0s → x = 1.6m ]

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Answer 2

Answer:

Explanation:

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