Question

The figure shows a graph of actual position-versus-time data for a particular type of drag racer known as a "funny car. Estimate the car's velocity at 2.0 sand 4.0 s.

$2_20.jpg$

Answer 1

The slope of the tangent line indicates the instantaneous velocity at that instant of time. Thus, the velocity of the car at \(2.0 \mathrm{~s}\) is,

$$ \begin{aligned} v_{2 x} &=\frac{\Delta x}{\Delta t} \\ &=\frac{200 \mathrm{~m}}{3 \mathrm{~s}} \\ &=66.7 \mathrm{~m} / \mathrm{s} \\ & \approx 67 \mathrm{~m} / \mathrm{s} \end{aligned} $$

The velocity of the car at \(4.0 \mathrm{~s}\) is,

$$ \begin{aligned} v_{4 x} &=\frac{\Delta x}{\Delta t} \\ &=\frac{400 \mathrm{~m}}{5 \mathrm{~s}-2 \mathrm{~s}} \\ &=133 \mathrm{~m} / \mathrm{s} \\ & \approx \mathbf{1 3 0} \mathrm{m} / \mathrm{s} \end{aligned} $$

Answer 2

velocity at 2.0 =67m/s
velocity at 4.0= 130m/s

Answer 3

The figure shows a graph of actual position-versus-time data for a particular type of drag racer known as a "funny car. Estimate the car's velocity at2.0 s and 4.0 s.

$2_20.jpg$

v(2) = tan 45 = 1 m /s

v(4 ) = tan 60 = 1.732 m/ s

Answer 4

[REMOVED]

Answer 5

[REMOVED]

Answer 6

Answer 7

The slope of the position verses time graph gives the velocity.

Write the expression for the slope of the position verses time.

The expression for velocity from the position verses time graph can also be written as,

Here, , are the positions and , are the time.

Instantaneous velocity is defined the velocity at the specific point of time.

…… (1)

Consider the following graph as,

$D:\Akash documents\akash9884\2016\August\06.08.2016\Rajeev\1.png$

If the velocity changes with time, the position- time graph will become a curved line, as in this case. The slope at any point of position-time graph represents velocity of the car at that point.

It is possible to make the graph show as a straight line by choosing a small enough time interval.

(a)

Consider the following figure for velocity at .

Calculate the car’s velocity at .

Substitute for and for in the equation (1).

Therefore, the approximate velocity at is.

(b)

Consider the following figure for velocity at .

Calculate the car’s velocity at .

Substitute for and for.

Therefore, the approximate velocity at is.