Question

A car starts from rest and accelerates to a speed of 60 mph in 12 sec. It travels 60 mph for 1 min and then decelerates for 20 sec until it comes to rest. The speed of the car s(t) (in ) at a time t (in sec) after the car begins motion can be modeled by:

Answer 1

The model of the speed of the car at different intervals is an illustration of piece-wise function.

• The speed of the car at 1 second is $\mathbf{\frac{5}{12}}$
• The speed of the car at 12 seconds is $\mathbf{\frac{5}{12}}$
• The speed of the car at 47 seconds is $\mathbf{\frac{5}{12}}$
• The speed of the car at 74 seconds is $\mathbf{\frac{5}{12}}$

(a) The speed at 1 second

This means that:

$\mathbf{t = 1}$

To do this, we make use of the following function:

$\mathbf{s(t) = \frac{5}{12}t^2}$

Because the domain covers $\mathbf{t = 1}$

So, we have:

$\mathbf{s(1) = \frac{5}{12} \times 1^2}$

$\mathbf{s(1) = \frac{5}{12} }$

(b) The speed at 12 seconds

This means that:

$\mathbf{t = 12}$

To do this, we make use of the following function:

$\mathbf{s(t) = \frac{5}{12}t^2}$

Because the domain covers $\mathbf{t = 12}$

So, we have:

$\mathbf{s(12) = \frac{5}{12} \times 12^2}$

$\mathbf{s(12) = 60}$

(c) The speed at 47 seconds

This means that:

$\mathbf{t = 47}$

To do this, we make use of the following function:

$\mathbf{s(t) = 60}$

Because the domain covers $\mathbf{t = 47}$

So, we have:

$\mathbf{s(47) = 60}$

(c) The speed at 74 seconds

This means that:

$\mathbf{t = 74}$

To do this, we make use of the following function:

$\mathbf{s(t) = \frac{3}{20}(92 - t)^2}$

Because the domain covers $\mathbf{t = 74}$

So, we have:

$\mathbf{s(74) = \frac{3}{20}(92 - 74)^2}$

$\mathbf{s(74) = \frac{3}{20} \times 18^2}$

$\mathbf{s(74) = \frac{3}{20} \times 324}$

$\mathbf{s(74) = \frac{3\times 324}{20} }$

$\mathbf{s(74) = \frac{972}{20} }$

$\mathbf{s(74) = 48.6}$

Hence, the speed at 74 seconds is 48.6 mph

Read more about piece-wise functions at:

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