At highway speeds, a particular automobile is capable of an acceleration of about 1.6 m/s2. At this rate, how long does it take to accelerate from 76 km/h to 118 km/h

To find out how long it takes to accelerate from 76 km/h to 118 km/h, we need to break the problem down into two steps:

Step 1: Convert the speeds from km/h to m/s.
Step 2: Use the formula of time, acceleration, and change in velocity to calculate the time taken to accelerate.

Let's tackle each step:

Step 1: Convert the speeds from km/h to m/s.
To convert km/h to m/s, we can use the conversion factor of 1 km/h = 0.2778 m/s.

Initial speed: 76 km/h = 76 × 0.2778 m/s = 21.1116 m/s (rounded to four decimal places)
Final speed: 118 km/h = 118 × 0.2778 m/s = 32.7778 m/s (rounded to four decimal places)

Step 2: Use the formula of time, acceleration, and change in velocity to calculate the time taken to accelerate.
The formula for calculating time is:

time = (Final velocity - Initial velocity) / acceleration

Substituting the values we calculated in Step 1:

time = (32.7778 m/s - 21.1116 m/s) / 1.6 m/s^2

Calculating the difference in velocity:

time = 11.6662 m/s / 1.6 m/s^2

Simplifying the division:

time = 7.2914 seconds (rounded to four decimal places)

Therefore, it will take approximately 7.2914 seconds to accelerate from 76 km/h to 118 km/h at an acceleration rate of 1.6 m/s^2.

Acceleration is just the speed at which the velocity changes. You know that every second the velocity increases by 1.6 m/s. So, what's the total change in velocity?

118-76 = 42 m/s

So, how many seconds does it take to change by 42, given a change of 1.6 every second?

42/1.6 = 26.25 sec