29.9k views
0 votes
The rate of change of speed for a ship is 0.25 m/s². If the speed of the ship after 1 minute is 78 km/h, what is its initial speed?​

User Ceilfors
by
8.0k points

1 Answer

3 votes

Answer:

6.67 meters/second
or equivalently
24 km/hour

Explanation:

The relationship between final velocity, initial velocity, acceleration and time is given by the equation
v = u + at

where

v = final velocity

u = initial velocity

a = acceleration

t = time from initial velocity to final velocity

We are given

v = 78 km/h

a = 0.25 m/s²

t = 1 minute

We are asked to find u, the initial velocity

Since each of the parameters are given in different units, the first step is get them all to a common unit

Let's convert everything to m/second and seconds

Since there are 1000 meters in 1 km and 3600 seconds in 1 hour ,

78 km/hour = 78 x 1000/3600 = 21.66667 meters per second which would be our value for v. Rounded to 2 decimals this would be 21.67 m/s

There are 60 seconds in 1 minute so our value for t = 1 minute x 60 = 60 second.

We finally have

v = 21.67 m/s

a = 0.25 m/s²

t = 60 seconds

Plug in known values in the equation

21.67 = u + 0.25 x 60

21.67 = u + 15

u + 15 = 21.67

u = 21.67 - 15 = 6.67 m/s

If you want to convert this back to km/hour multiply by 3600 and divide by 1000

u = 6.67 x 3600/1000 = 24.012 km/hour or rounded to 24 km/hour

User Dororo
by
7.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories