The maker of an automobile advertises that it takes 13 seconds to accelerate from 25 kilometers per hour to 90 kilometers per hour. Assuming constant acceleration, compute the following.
The acceleration in m/s^2
The distance the car travels during the 13 seconds
watch out, km/hour given
forgot to change the units from km/h to m/s
go with Damon's answers
a = (V2-V1)/(t2-t1)
V2 = 90,000/3600 = 25 m/s
V1 = 25,000/3600 = 6.94
t2-t1 = 13
so a = 1.39 m/s^2
======================
d = V1 t + (1/2)a t^2
= 6.94 *13 + .695*169
= 208 m
Why did the car get a speeding ticket? Because it couldn't stop IN-TIME-ir! But let's calculate the acceleration and distance for you, Speedy Gonzales!
First, let's convert the speeds from km/h to m/s.
Initial speed (v₀) = 25 km/h
Final speed (v) = 90 km/h
In m/s, the initial speed is:
v₀ = 25 km/h = 25 * (1000/3600) m/s ≈ 6.94 m/s
The final speed in m/s is:
v = 90 km/h = 90 * (1000/3600) m/s ≈ 25 m/s
Next, the time taken (t) is given as 13 seconds.
The formula to calculate acceleration (a) is:
a = (v - v₀) / t
Using the values we have, we can plug them into the formula:
a = (25 m/s - 6.94 m/s) / 13 s ≈ 1.34 m/s²
So, the acceleration is approximately 1.34 m/s².
To find the distance (d) traveled during the 13 seconds, we can use the formula:
d = v₀t + 0.5at²
Substituting the values in, we get:
d = (6.94 m/s)(13 s) + 0.5(1.34 m/s²)(13 s)² ≈ 174.62 m
Therefore, the car travels approximately 174.62 meters during those 13 seconds.
Hope that clears things up, Speedy! Keep the laughter rolling on the road! 🤡🚗
To find the acceleration in m/s^2, we need to convert the given speeds from kilometers per hour (km/h) to meters per second (m/s) and then use the formula for acceleration.
1. Convert 25 km/h to m/s:
To convert from km/h to m/s, we divide by 3.6, since there are 3.6 seconds in one hour:
25 km/h ÷ 3.6 = 6.94 m/s (rounded to two decimal places)
2. Convert 90 km/h to m/s:
90 km/h ÷ 3.6 = 25 m/s
Next, we can use the formula for acceleration:
acceleration (a) = change in velocity (Δv) / change in time (Δt)
Given that the time is 13 seconds and the initial velocity is 6.94 m/s, and the final velocity is 25 m/s, we can substitute these values into the formula:
acceleration (a) = (25 m/s - 6.94 m/s) / 13 s ≈ 1.27 m/s^2 (rounded to two decimal places)
Therefore, the acceleration of the car is approximately 1.27 m/s^2.
To find the distance the car traveled during the 13 seconds, we can use another formula:
distance (d) = initial velocity (v0) * time (t) + 0.5 * acceleration (a) * time^2
Substituting the values:
initial velocity (v0) = 6.94 m/s
acceleration (a) = 1.27 m/s^2
time (t) = 13 s
distance (d) = 6.94 m/s * 13 s + 0.5 * 1.27 m/s^2 * (13 s)^2
distance (d) = 90.22 m + 1.67 m ≈ 91.89 m (rounded to two decimal places)
Therefore, the car travels approximately 91.89 meters during the 13 seconds.
if we have acceleration of a, then
v = at + c
case1: when t=0, v=25
25 = 0+c ---> v = at + 25
so when t = 13, v = 90
90 = 13a + 25
a = 65/13 = 5 m/s^2 -----> v = 5t + 25
distance = (5/2)t^2 + 25t + k
when t=0 , distance = 0 , so k = 0
distance = (5/2)t^2 + 25t
when t = 13
distance = (5/2)(169) + 25(13) = 747.5 m
also see the first four of the Related Questions below