# An object with a mass of #3 kg# is acted on by two forces. The first is #F_1= < 7 N , -3 N># and the second is #F_2 = < -1 N, 6 N>#. What is the object's rate and direction of acceleration?

##### 1 Answer

The objects rate of acceleration is

The direction of the acceleration is at an angle of

#### Explanation:

Let the resultant force acting on the object be

# vecF = vecF_1 + vecF_2#

# \ \ \ \ = <<7,-3>> + <<-1,6>>#

# \ \ \ \ = <<6,3>>#

The magnitude,

# F = | vecF | #

# \ \ \ \= |<<6,3>>| #

# \ \ \ \= sqrt(6^2+3^2) #

# \ \ \ \= sqrt(36+9) #

# \ \ \ \= sqrt(45) #

# \ \ \ \= 6.71 \ N # (2dp)

Applying Newton's 2nd Law of Motion,

# :. 6.71=3a#

# :. a=2.24 \ ms^-2# (2dp)

The direction of the acceleration is the same as the direction of the resultant force

# tan theta = 3/6 #

# :. \ theta = arctan 0.5#

# :. \ theta = 26.6º# (1dp)

Hence,

The objects rate of acceleration is

#2.23 \ ms^-2# (2dp)

The direction of the acceleration is at an angle of#26.6º# (1dp)